Type IIP supernovae as cosmological probes: A SEAM distance to SN1999em

arXiv:astro-ph/0410153 v1 6 Oct 2004

and PeterH. Haushildt

4 yetihs.uni-hamburg.de

ABSTRACT

Due to their intrinsi brightness, sup ernovae make exellent osmologial

prob es. We desrib e the SEAM metho d for obtaining distanes to Typ e I IP

su-p ernovae(SNeI IP)andpresentadistanetoSN1999emforwhihaCepheid

dis-taneexists. Ourmo delsgiveresults onsistentwith the Cepheiddistane,even

though we have not attempted to tune the underlying hydro dynamial mo del,

wehavesimplyhosentheb estts. This isinontradistintiontothe expanding

photosphere metho d (EPM) whih yields a distane to SN 1999em that is 50%

smallerthantheCepheiddistane. Weemphasizethedierenesb etweenSEAM

andEPM. Weshow thatthedilution fatorsused intheEPM analysiswere

sys-tematially to o small at later ep o hs. We also show that the EPM blakb o dy

assumption issusp et.

SineSNeI IParevisibletoredshiftsas highasz

<6,withthe JWST,SEAM

may b e a valuableprob e ofthe earlyuniverse.

1

DepartmentofPhysis and Astronomy,University ofOklahoma,440West Bro oks,Rm.131,Norman,

OK73019,USA

2

ComputationalResearh Division,Lawrene Berkeley NationalLab oratory,MS50F-1650, 1Cylotron

Rd,Berkeley,CA94720-8139USA

3

Lab oratoirede PhysiqueNuleaire etdeHaute Energies, CNRS-IN2P3,UniversityofParis VI I,Paris,

Frane 4

Subjetheadings: osmology: distanesale|stars: atmospheres|sup ernovae:

SN 1999em

1. Distanes from Supernovae

A reliable way to determineaurate distanes is a Holy Grail of astronomy and

par-tiularly osmology. In order to determinethe values of the fundamentalosmologial

pa-rameters,an aurate distaneindiator visibleto highredshift is required. Sup ernovae are

extremely bright and hene an b e deteted at osmologial distanes with mo dern large

telesop es. Due to their homogeneity, SNe Ia had long b een thought of as as go o d

dis-taneindiators sinetheyroughly meetthe astronomer'sdenition ofa\standard andle",

that is that the luminosity at p eak, L

max

, is approximately onstant. Two Hubble Spae

Telesop e (HST) projets (Freedman et al. 2001; Paro di et al. 2000) were awarded time

to use Cepheid variable stars to determine distanes to the Virgo luster and to determine

the Hubble onstant to 10% auray. An additional aim of the program of Sandage and

ollab orators (Paro di et al. 2000) was to alibrate the luminosity of SNe Ia by obtaining

Cepheiddistanes to galaxieswhihalso werethe hostsof SNeIa. Distanesobtained using

Cepheids are onsidered to b e the among the most reliable in astronomy (purely

trigono-metri metho ds annot b e used at distanes in the Hubble ow), but they are not free of

systematierrorsandCepheidsareto o dimto b eobservedat largedistanes. Thereliability

ofSNeIaas distaneindiators improvedsigniantlywiththe realizationthatthe

luminos-ity at p eak was orrelated with the width of the light urve(Phillips 1993) and hene that

SNeIawereorretableandlesinmuhthesamewaythatCepheidsare(Phillipsetal.1999;

Goldhab er et al.2001; Riessetal. 1995). This work and the developmentof highlyeÆient

searh strategies (Perlmutteret al. 1997) sparkedtwo groups to use SNe Ia to measure the

deeleration parameterand to disoverthe dark energy (Riess et al.1998; Perlmutteret al.

1999).

AlloftheworkwithSNeIaisempirial,basedonobservedSNeIatemplatelighturves.

Another metho d of determining distanes using sup ernovae is the \expanding photosphere

metho d" (EPM, Kirshner & Kwan 1974; Branh et al. 1981; Eastman & Kirshner 1989;

Eastman et al. 1996) a variation of the Baade-Wesselink metho d (Baade 1926). The EPM

metho d assumes that for SNe I IP, with intat hydrogen envelop es, the sp etrum is not far

fromthat ofa blakb o dyand hene the luminosityis approximatelygivenby

L=4 2 R 2 T 4

radia-dominated atmosphere the blakb o dy is diluted(Hershkowitz, Linder, &Wagoner 1986a,b;

Hershkowitz & Wagoner 1987). The temp erature is found from observed olors, so in fat

is a olor temp erature and not an eetive temp erature, the photospheri velo ity an b e

estimatedfrom observedsp etra using the velo itiesof the weakestlines,

R=vt;

the dilutionfator is estimatedfrom syntheti sp etral mo dels, and t omes fromthe light

urve and demanding self-onsisteny.

Both an advantage and disadvantage of EPM is that itprimarilyrequires photometry.

Sp etraare onlyusedto determinethephotospherivelo ity,olorsyieldtheolortemp

era-ture,whihinturnisusedtodeterminetheappropriatedilutionfator (frommo delresults).

This metho d suers from unertainties in determiningthe dilution fators, the diÆulty of

knowing whih linesto use as velo ity indiators, unertaintiesb etweenolor temp eratures

and eetive temp eratures,and questions of how to maththe photospheri radius used in

themo delsto determinethedilutionfatorandtheradiusofthelineformingregion(Hamuy

et al.2001; Leonard et al. 2002). In spite of this the EPM metho dwas suessfully applied

to SN1987A inthe LMC(Eastman&Kirshner1989;Branh1987) whihledto hop es that

the EPM metho d would lead to aurate distanes, indep endent of other astronomial

al-ibrators. Reently,the EPM metho d was appliedto the very well observedSN I IP 1999em

(Hamuyet al.2001; Leonard et al. 2002; Elmhamdi etal. 2003). All three groups found a

distaneof 7.5{8.0 Mp . Leonard etal.(2003) subsequently used HST to obtaina Cepheid

distaneto the parent galaxyof SN1999em,NGC 1637,and found 11:71:0 Mp , avalue

50% larger than that obtained with EPM.

With mo dern detailedNLTE radiativetransfer o des, aurate syntheti sp etra of all

typ esofsup ernovaeanb ealulated. TheSp etral-ttingExpandingAtmosphereMetho d

(SEAM,Baron etal.1995,1996;Lentzetal.2001;Mithelletal.2002) was develop edusing

the generalized stellar atmosphereo de PHOENIX(for a reviewofthe o deseeHaushildt&

Baron 1999). WhileSEAM is similarto EPM in spirit, it avoids the use of dilution fators

and olor temp eratures. Velo ities are determined aurately by atually tting syntheti

and observed sp etra. The radius is still determined by the relationship R = vt, (whih

is an exellentapproximation b eause all sup ernovae quiklyreah homologous expansion)

and the explosiontime isfound by demandingself onsisteny. SEAM uses all the sp etral

information available in the observed sp etra simultaneously whih broadens the base of

parameter determination. Sine the sp etral energy distribution is known ompletelyfrom

the alulated syntheti sp etra, one may alulate the absolute magnitude, M

X , in any photometri band X, M X = 2:5log Z 1 S X ()L d+C X

where S X

is the resp onse of lter X, L

is the luminosity p er unit wavelength, and C

X is

the zero p oint of lter X determinedfrom standard stars. Then one immediatelyobtains a

distanemo dulus

X

, whihisa measure ofthe distane

X m X M X A X =5log(d=10p ); wherem X

isthe apparentmagnitude inband X and A

X

istheextintiondue to dust along

the lineof sight b oth in the host galaxy and in our own galaxy. Baron et al.(2000) found

that the earlysp etra werequitesensitiveto the assumed reddening and hene determined

a value of E(B V) =0:1 for SN 1999em. The SEAM metho d do es not need to invokea

blakb o dyassumption or to alulatedilution fators.

2. Results

We used the ab ove metho d to alulate the distane to SN 1999em. The mo delswere

takenfromMo delS15of Wo osley&Weaver(1995). Themo delwasexpandedhomologously

and the gamma-ray dep osition was parameterized to b e onsistent with the nikel mixing

found in SN 1987A (Mithell et al. 2001). The abundanes were taken diretly from the

mo del, and the eets of radioative deay were taken into aount. The results are

sum-marized in Table 1. The explosion date is given as the numb er of days prior to disovery

on 1999 Otob er 29 (HJD 2451480.94). We used observed photometry of Leonard et al.

(2002) and Hamuyet al.(2001) in UBVRIZ. The quotederrors are the 1 error in the

determination of the mean distane, whih we b elieve are reasonably aurate estimates of

the true error whih is diÆult to determine formally. For our favored value (see b elow) of

12:5Mp wendaformalerrorof1:8Mp ifweaddinquadraturetheerrorindetermining

the eetive temp erature(500 K),the error in determiningthe velo ity (500 km s

1 ),

and the formal errorin the mean.

Table 1. Data Set D (Mp ) t exp 5ep o hs inludingU 30:070:8 10:34:5 5:20:4 5ep o hs exludingU 30:470:39 12:42:4 5:90:3 5ep o hs exludingU on 5th ep o h 30:490:36 12:52:3 5:90:3

Figure1omparesobservedandmo delsp etra,detailsofthemo delingwillb edisussed

elsewhere. Overall the ts are exellent,exepton Novemb er28 where the blue part of the

sp etrum isp o orly t,this isdue to the fat that at this late timethe sp etrum formsover

amuhlargermassrangeofthe ejetaandso wearesensitiveto thedetailedmixingofb oth

nikel and heliumwhih we have not attempted to adjust in the mo dels. If we exludethe

U band from the alulation the satter is onsiderably redued. Additionally, when the U

bandisinludedtheinferredexplosiondateisnearertothedateofdisoverywhihpro dues

a systemati rise in the SEAM distane with time. Errors in the explosion date primarily

aet the absolute magnitudes of the early sp etral mo delssine they are moresensitive to

errors in the explosion date than are later ep o hs. If the estimated time from explosion is

to o small, the mo delswill have radii whih are to o small (R = vt). Withsmaller emitting

area, they will b e dimmerand hene app ear to b e loser.The results of negleting the U

band entirelyare nearlyidential with those if weinlude the U data exeptfor the one on

Novemb er28. The abilityto omparesynthetisp etrawith observationalsp etra islearly

anadvantageoftheSEAMmetho d. Thus,weadopttheresultsoftheb ottomlineofTable1,

whih is in go o d agreementwith the Cepheid result and show that quality ts to SNe I IP

an givedistanes aurate to 20%, without adjusting metaliities, helium mixing, or nikel

mixing. One we have ompleted a large grid of mo dels whih vary these parameters we

should b e able to redue the unertainties evenmore,thus SNe I IP will b eomeimp ortant

osmologial prob es.

3. Disussion

The SEAM metho d assumes that sup ernovae are spherially symmetri, whih is not

stritly true. However, p olarization data indiate that SNe I IP seem to b e more

spheri-ally symmetrithan other typ es of ore ollapsesup ernovae, most likely b eause the large

intat hydrogen envelop e spheriizes the explosion. Thus SNe I IP app ear to b e the most

promising andidates for using the SEAM metho d. Leonard et al. (2001) found evidene

for p olarization in SN 1999em at 7{163 days after disovery. Mo deled in terms of oblate

eletron sattering atmospheres,the aspheriity was ab out 7%. They found sometendeny

for inreasing p olarization with time. This is onsistent with p olarization studies of Typ e

Ib/sup ernovaewherethe p olarizationapp ears to inreasetheloserone getsto the entral

explosion mehanism(Wang etal. 2003).

It is diÆultto knowexatly why the SEAMmetho d givessuh adierent resultfrom

that of EPM. Leonard et al. (2002) found t

exp

=5:3 d, and our date is somewhat earlier.

Fig. 1.| Thesynthetisp etra(dashed lines)are omparedtoobservedsp etra(solidlines)

at 5 dierentep o hs. The observed sp etra were obtained at CTIO for Ot 30, Nov 2, and

Nov18 (Hamuyetal.2001), atHST andFLWOonNov5(Baronetal.2000) andtheoptial

sp etrum on Nov 28 was obtained at Lik (Leonard et al. 2002) while the IR was obtained

the olor temp erature T BV

, the velo ity at the photosphere (dened as = 2=3), and the

dilution fator,

BV

, obtained using T

BV

with those of Hamuy et al. (2001). The results

agreeverywellat earlytimes,butbythe4th ep o hthe dilutionfatorsdisagreeby40% and

bynearlyafatorof3at thefthep o h. Comparingonlytwoep o hs,if onemistakenlyuses

adilution fator that isto o smallat the latertime,the distane obtained willb eto o small.

WithhindsightHamuyetal.(2001)reognizedthis fatwhentheyfoundthattheyobtained

distanes loseto the Cepheidvalue whentheyrestritedtheiranalysisto earlytimeswhere

ourdilutionfatorsagree. However,thewholefoundation ofEPMapp earssusp et. Figure3

omparestheb esttdilutedPlankfuntionwithouromputeduxattherstep o hwhere

wehavetthe observationsverywell. ItislearthataPlankfuntiondo esnot ttheSED

at all. Thus, we nd that the diluted blakb o dy assumption is to o simplisti, partiularly

at later times. That the EPMapproahworks at earlytimesseemsoinidental,but itmay

b ethat inthe hotearlyphasesthe olortemp eratureis reasonablyaurate, wewillexplore

this in detail infuture work.

The SEAM metho d seemslearlysup erior to EPM sine the assumption of blak-b o dy

emissionisneverrealizedinasup ernova. SEAMshouldb etestablebytheNearbySup ernova

Fatory (Aldering et al. 2002) if they follow a dozen or so SNeI IP inthe Hubble ow that

they willdisover. Anindep endent osmologialprob e ishighlydesirable.

SNe I IP may b e detetable to high redshifts with the James Webb Spae Telesop e

(JWST). With a dataset of sp etral mo dels that t nearby SNe I IP we will b e able to

determinethe nuleosyntheti history of the rst generation of stars.

We thank Doug Leonard and Mario Hamuyfor helpfuldisussions on SN 1999em and

Typ e I IP sup ernovae. We thank the referee,Adam Riessfor improvingthe presentation of

this work. This work was supp orted in part by by NASA grant NAG5-3505, NSF grants

AST-0204771 and AST-0307323, an IBM SUR grant to the University of Oklahoma and

by NASA grants NAG 5-8425 and NAG 5-3619 to the University of Georgia. PHH was

supp orted in part by the P^ole Sientiquede Mo delisation Numeriqueat ENS-Lyon. This

researh used resoures of: the San Diego Sup eromputer Center (SDSC), supp orted by

the NSF; the National Energy Researh Sienti Computing Center (NERSC), whih is

supp orted by the OÆe of Siene of the U.S. Department of Energy under Contrat No.

DE-AC03-76SF00098 ; and the Hohstleistungs RehenzentrumNord (HLRN).We thank all

Fig. 2.| The EPM parameters v( = 2=3), T BV

, and dilution fator

BV

from our mo dels

(lledirles)are omparedwith thoseofHamuyetal.(2001) (lled triangles). Whilethere

Fig. 3.| Theuxfrom ourmo del(solid line)omparedwith the b esttdiluted blakb o dy

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