The Accelerating Universe and Dark Energy Evidence from Type Ia Supernovae

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The Accelerating Universe and Dark Energy:Evidence from Type Ia Supernovae Alexei V.Filippenko Department of Astronomy,University of California,Berkeley,CA 94720-3411,USA (email:alex@https://www.sodocs.net/doc/7c6228056.html,)Summary.I discuss the use of Type Ia supernovae (SNe Ia)for cosmological dis-tance determinations.Low-redshift SNe Ia (z <～0.1)demonstrate that the Hubble expansion is linear,that H 0=72±8km s ?1Mpc ?1,and that the properties of dust in other galaxies are similar to those of dust in the Milky Way.The light curves of high-redshift (z =0.3–1)SNe Ia are stretched in a manner consistent with the expansion of space;similarly,their spectra exhibit slower temporal evolu-tion (by a factor of 1+z )than those of nearby SNe Ia.The measured luminosity distances of SNe Ia as a function of redshift have shown that the expansion of the Universe is currently accelerating,probably due to the presence of repulsive dark energy such as Einstein’s cosmological constant (Λ).From about 200SNe Ia,we ?nd that H 0t 0=0.96±0.04,and ?Λ?1.4?M =0.35±https://www.sodocs.net/doc/7c6228056.html,bining our data with the results of large-scale structure surveys,we ?nd a best ?t for ?M and ?Λof 0.28and 0.72,respectively —essentially identical to the recent WMAP results (and having comparable precision).The sum of the densities,～1.0,agrees with extensive measurements of the cosmic microwave background radiation,including WMAP ,and coincides with the value predicted by most in?ationary models for the early Universe:the Universe is ?at on large scales.A number of possible system-atic e?ects (dust,supernova evolution)thus far do not seem to eliminate the need for ?Λ>0.However,during the past few years some very peculiar low-redshift SNe Ia have been discovered,and we must be mindful of possible systematic e?ects if such objects are more abundant at high redshifts.Recently,analyses of SNe Ia at z =1.0–1.7provide further support for current acceleration,and give tentative evidence for an early epoch of deceleration.The dynamical age of the Universe is estimated to be 13.1±1.5Gyr,consistent with the ages of globular star clusters and with the WMAP result of 13.7±0.2Gyr.Current projects include the search for additional SNe Ia at z >1to con?rm the early deceleration,and the measurement of a few hundred SNe Ia at z =0.2–0.8to more accurately determine the equation of state of the dark energy,w =P/(ρc 2),whose value is now constrained by SNe Ia

to be in the range ?1.48<～w <～?0.72at 95%con?dence.1Introduction

Supernovae (SNe)come in two main varieties (see Filippenko 1997b for a review).Those whose optical spectra exhibit hydrogen are classi?ed as Type II,while hydrogen-de?cient SNe are designated Type I.SNe I are further subdivided according to the appearance of the early-time spectrum:SNe Ia

2Alexei V.Filippenko

are characterized by strong absorption near6150?A(now attributed to Si II), SNe Ib lack this feature but instead show prominent He I lines,and SNe Ic have neither the Si II nor the He I lines.SNe Ia are believed to result from the thermonuclear disruption of carbon-oxygen white dwarfs,while SNe II come from core collapse in massive supergiant stars.The latter mechanism probably produces most SNe Ib/Ic as well,but the progenitor stars previously lost their outer layers of hydrogen or even helium.

It has long been recognized that SNe Ia may be very useful distance indicators for a number of reasons;see Branch&Tammann(1992),Branch (1998),and references therein.(1)They are exceedingly luminous,with peak M B averaging?19.0mag if H0=72km s?1Mpc?1.(2)“Normal”SNe Ia have small dispersion among their peak absolute magnitudes(σ<～0.3mag).

(3)Our understanding of the progenitors and explosion mechanism of SNe Ia is on a reasonably?rm physical basis.(4)Little cosmic evolution is expected in the peak luminosities of SNe Ia,and it can be modeled.This makes SNe Ia superior to galaxies as distance indicators.(5)One can perform local tests of various possible complications and evolutionary e?ects by comparing nearby SNe Ia in di?erent environments.

Research on SNe Ia in the1990s has demonstrated their enormous poten-tial as cosmological distance indicators.Although there are subtle e?ects that must indeed be taken into account,it appears that SNe Ia provide among the most accurate values of H0,q0(the deceleration parameter),?M(the matter density),and?Λ[the cosmological constant,Λc2/(3H20)].

There have been two major teams involved in the systematic investi-gation of high-redshift SNe Ia for cosmological purposes.The“Supernova Cosmology Project”(SCP)is led by Saul Perlmutter of the Lawrence Berke-ley Laboratory,while the“High-Z Supernova Search Team”(HZT)is led by Brian Schmidt of the Mt.Stromlo and Siding Springs Observatories.I have been privileged to work with both teams(see Filippenko2001for a personal account),but my primary allegiance is now with the HZT.

2Homogeneity and Heterogeneity

Until the mid-1990s,the traditional way in which SNe Ia were used for cosmo-logical distance determinations was to assume that they are perfect“standard candles”and to compare their observed peak brightness with those of SNe Ia in galaxies whose distances had been independently determined(e.g.,with Cepheid variables).The rationale was that SNe Ia exhibit relatively little scatter in their peak blue luminosity(σB≈0.4–0.5mag;Branch&Miller 1993),and even less if“peculiar”or highly reddened objects were eliminated from consideration by using a color cut.Moreover,the optical spectra of SNe Ia are usually rather homogeneous,if care is taken to compare objects at similar times relative to maximum brightness(Riess et al.1997,and ref-

The Accelerating Universe3 erences therein).Over80%of all SNe Ia discovered through the early1990s were“normal”(Branch,Fisher,&Nugent1993).

From a Hubble diagram constructed with unreddened,moderately distant SNe Ia(z<～0.1)for which peculiar motions are small and relative distances (given by ratios of redshifts)are accurate,Vaughan et al.(1995)?nd that M B(max) =(?19.74±0.06)+5log(H0/50)mag.(1) In a series of papers,Sandage et al.(1996)and Saha et al.(1997)combine similar relations with Hubble Space Telescope(HST)Cepheid distances to the host galaxies of seven SNe Ia to derive H0=57±4km s?1Mpc?1.

Over the past two decades it has become clear,however,that SNe Ia do not constitute a perfectly homogeneous subclass(e.g.,Filippenko1997a,b). In retrospect this should have been obvious:the Hubble diagram for SNe Ia exhibits scatter larger than the photometric errors,the dispersion actually rises when reddening corrections are applied(under the assumption that all SNe Ia have uniform,very blue intrinsic colors at maximum;van den Bergh& Pazder1992;Sandage&Tammann1993),and there are some signi?cant out-liers whose anomalous magnitudes cannot be explained by extinction alone.

Spectroscopic and photometric peculiarities have been noted with increas-ing frequency in well-observed SNe Ia.A striking case is SN1991T;its pre-maximum spectrum did not exhibit Si II or Ca II absorption lines,yet two months past maximum brightness the spectrum was nearly indistinguishable from that of a classical SN Ia(Filippenko et al.1992b;Phillips et al.1993). The light curves of SN1991T were slightly broader than the SN Ia tem-plate curves,and the object was probably somewhat more luminous than average at maximum.Another well-observed,peculiar SNe Ia is SN1991bg (Filippenko et al.1992a;Leibundgut et al.1993;Turatto et al.1996).At maximum brightness it was subluminous by1.6mag in V and2.5mag in B, its colors were intrinsically red,and its spectrum was peculiar(with a deep absorption trough due to Ti II).Moreover,the decline from maximum was very steep,the I-band light curve did not exhibit a secondary maximum like normal SNe Ia,and the velocity of the ejecta was unusually low.The photo-metric heterogeneity among SNe Ia is well demonstrated by Suntze?(1996) with objects having excellent BV RI light curves.

3Cosmological Uses:Low Redshifts

Although SNe Ia can no longer be considered perfect“standard candles,”they are still exceptionally useful for cosmological distance determinations. Excluding those of low luminosity(which are hard to?nd,especially at large distances),most of the nearby SNe Ia that had been discovered through the early1990s were nearly standard(Branch et al.1993;but see Li et al.2001b for more recent evidence of a higher intrinsic peculiarity rate).Also,after

4Alexei V.Filippenko

many tenuous suggestions(e.g.,Pskovskii1977,1984;Branch1981),Phillips (1993)found convincing evidence for a correlation between light curve shape and the luminosity at maximum brightness by quantifying the photomet-ric di?erences among a set of nine well-observed SNe Ia,using a parameter [?m15(B)]that measures the total drop(in B magnitudes)from B-band maximum to t=15days later.In all cases the host galaxies of his SNe Ia have accurate relative distances from surface brightness?uctuations or from the Tully-Fisher relation.The intrinsically bright SNe Ia clearly decline more slowly than dim ones,but the correlation is stronger in B than in V or I.

Using SNe Ia discovered during the Cal′a n/Tololo survey(z<～0.1),Hamuy et al.(1995,1996b)re?ne the Phillips(1993)correlation between peak lumi-nosity and?m15(B).Apparently the slope is steep only at low luminosities; thus,objects such as SN1991bg skew the slope of the best-?tting single straight line.Hamuy et al.reduce the scatter in the Hubble diagram of nor-mal,unreddened SNe Ia to only0.17mag in B and0.14mag in V;see also Tripp(1997).Yet another parameterization is the“stretch”method of Perl-mutter et al.(1997)and Goldhaber et al.(2001):the B-band light curves of SNe Ia appear nearly identical when expanded or contracted temporally by a factor(1+s),where the value of s varies among objects.In a similar but distinct e?ort,Riess,Press,&Kirshner(1995)show that the luminosity of SNe Ia correlates with the detailed shape of the overall light curve.

By using light curve shapes measured through several di?erent?lters, Riess,Press,&Kirshner(1996a)extend their analysis and objectively elimi-nate the e?ects of interstellar extinction:a SN Ia that has an unusually red B?V color at maximum brightness is assumed to be intrinsically sublumi-nous if its light curves rise and decline quickly,or of normal luminosity but signi?cantly reddened if its light curves rise and decline more slowly.With a set of20SNe Ia consisting of the Cal′a n/Tololo sample and their own objects, they show that the dispersion decreases from0.52mag to0.12mag after ap-plication of this“multi-color light curve shape”(MLCS)method.The results from an expanded set of nearly50SNe Ia indicate that the dispersion de-creases from0.44mag to0.15mag(Figure1).The resulting Hubble constant is65±2(statistical)±7(systematic)km s?1Mpc?1,with an additional systematic and zeropoint uncertainty of±5km s?1Mpc?1.(Re-calibrations of the Cepheid distance scale,and other recent re?nements,lead to a best estimate of H0=72±8km s?1Mpc?1,where the error bar includes both statistical and systematic uncertainties;Parodi et al.2000;Freeman et al. 2001.)Riess et al.(1996a)also show that the Hubble?ow is remarkably lin-ear;indeed,SNe Ia now constitute the best evidence for linearity.Finally, they argue that the dust a?ecting SNe Ia is not of circumstellar origin,and show quantitatively that the extinction curve in external galaxies typically does not di?er from that in the Milky Way(cf.Branch&Tammann1992, but see Tripp1998).

The Accelerating Universe 5

(m -M )Log v (km/s)(m -M )Figure 1:Hubble diagrams for SNe Ia (A.G.Riess 2001,private commu-nication)with velocities (km s ?1)in the COBE rest frame on the Cepheid distance scale.The ordinate shows distance modulus,m ?M (mag).Top:The objects are assumed to be standard candles and there is no correction for extinction;the result is σ=0.42mag and H 0=58±8km s ?1Mpc ?1.Bottom:The same objects,after correction for reddening and intrinsic di?er-ences in luminosity.The result is σ=0.15mag and H 0=65±2(statistical)km s ?1Mpc ?1,subject to changes in the zeropoint of the Cepheid distance scale.(Indeed,the latest results with SNe Ia favor H 0=72km s ?1Mpc ?1.)

The advantage of systematically correcting the luminosities of SNe Ia at high redshifts rather than trying to isolate “normal”ones seems clear in view of evidence that the luminosity of SNe Ia may be a function of stellar population.If the most luminous SNe Ia occur in young stellar populations (e.g.,Hamuy et al.1996a,2000;Branch,Baron,&Romanishin 1996;Ivanov,Hamuy,&Pinto 2000),then we might expect the mean peak luminosity of high-z SNe Ia to di?er from that of a local sample.Alternatively,the use of Cepheids (Population I objects)to calibrate local SNe Ia can lead to a zeropoint that is too luminous.On the other hand,as long as the physics

6Alexei V.Filippenko

of SNe Ia is essentially the same in young stellar populations locally and at high redshift,we should be able to adopt the luminosity correction methods (photometric and spectroscopic)found from detailed studies of low-z SNe Ia.

Large numbers of nearby SNe Ia are now being found by my team’s Lick Observatory Supernova Search(LOSS)conducted with the0.76-m Katzman Automatic Imaging Telescope(KAIT;Li et al.2000;Filippenko et al.2001; Filippenko2003;see https://www.sodocs.net/doc/7c6228056.html,/～bait/kait.html).CCD im-ages are taken of～1000galaxies per night and compared with KAIT“tem-plate images”obtained earlier;the templates are automatically subtracted from the new images and analyzed with computer software.The system re-observes the best candidates the same night,to eliminate star-like cosmic rays,asteroids,and other sources of false alarms.The next day,undergrad-uate students at UC Berkeley examine all candidates,including weak ones, and they glance at all subtracted images to locate SNe that might be near bright,poorly subtracted stars or galactic nuclei.LOSS discovered20SNe (of all types)in1998,40in1999,38in2000,68in2001,and82in2002,mak-ing it by far the world’s leading search for nearby SNe.The most important objects were photometrically monitored through BV RI(and sometimes U)?lters(e.g.,Li et al.2001a,2003;Modjaz et al.2001;Leonard et al.2002a,b), and un?ltered follow-up observations(e.g.,Matheson et al.2001)were made of most of them during the course of the SN search.This growing sample of well-observed SNe Ia should allow us to more precisely calibrate the MLCS method,as well as to look for correlations between the observed properties of the SNe and their environment(Hubble type of host galaxy,metallicity, stellar population,etc.).

4Cosmological Uses:High Redshifts

These same techniques can be applied to construct a Hubble diagram with high-redshift SNe Ia,from which the value of q0=(?M/2)??Λcan be determined.With enough objects spanning a range of redshifts,we can mea-sure?M and?Λindependently(e.g.,Goobar&Perlmutter1995).Contours of peak apparent R-band magnitude for SNe Ia at two redshifts have di?er-ent slopes in the?M–?Λplane,and the regions of intersection provide the answers we seek.

4.1The Search

Based on the pioneering work of Norgaard-Nielsen et al.(1989),whose goal was to?nd SNe in moderate-redshift clusters of galaxies,the SCP(Perlmutter et al.1995a,1997)and the HZT(Schmidt et al.1998)devised a strategy that almost guarantees the discovery of many faint,distant SNe Ia“on demand,”during a predetermined set of nights.This“batch”approach to studying distant SNe allows follow-up spectroscopy and photometry to be scheduled in

The Accelerating Universe7 advance,resulting in a systematic study not possible with random discoveries. Most of the searched?elds are equatorial,permitting follow-up from both hemispheres.The SCP was the?rst group to convincingly demonstrate the ability to?nd SNe in batches.

Our approach is simple in principle;see Schmidt et al.(1998)for details, and for a description of our?rst high-redshift SN Ia(SN1995K).Pairs of?rst-epoch images are obtained with wide-?eld cameras on large telescopes(e.g., the Big Throughput Camera on the CTIO4-m Blanco telescope)during the nights around new moon,followed by second-epoch images3–4weeks later. (Pairs of images permit removal of cosmic rays,asteroids,and distant Kuiper-belt objects.)These are compared immediately using well-tested software, and new SN candidates are identi?ed in the second-epoch images(Figure 2).Spectra are obtained as soon as possible after discovery to verify that the objects are SNe Ia and determine their redshifts.Each team has already found over nearly200SNe in concentrated batches,as reported in numerous IAU Circulars(e.g.,Perlmutter et al.1995b,11SNe with0.16<～z<～0.65; Suntze?et al.1996,17SNe with0.09<～z<～0.84).The observed SN Ia rate at z≈0.5is consistent with the low-z SN Ia rate together with plausible star-formation histories(Pain et al.2002;Tonry et al.2003),but the error bars on the high-z rate are still quite large.

Figure2:Discovery image of SN1997cj(28April1997),along with the tem-plate image and an HST image obtained subsequently.The net(subtracted) image is also shown.

8Alexei V.Filippenko

Intensive photometry of the SNe Ia commences within a few days after procurement of the second-epoch images;it is continued throughout the en-suing and subsequent dark runs.In a few cases HST images are obtained.As expected,most of the discoveries are on the rise or near maximum bright-ness.When possible,the SNe are observed in?lters that closely match the redshifted B and V bands;this way,the K-corrections become only a second-order e?ect(Kim,Goobar,&Perlmutter1996;Nugent,Kim,&Perlmutter 2002).We try to obtain excellent multi-color light curves,so that reddening and luminosity corrections can be applied(Riess et al.1996a;Hamuy et al. 1996a,b).

Although SNe in the magnitude range22–22.5can sometimes be spec-troscopically con?rmed with4-m class telescopes,the signal-to-noise ratios are low,even after several hours of integration.Certainly Keck,Gemini,the VLT,or Magellan are required for the fainter objects(22.5–24.5mag).With the largest telescopes,not only can we rapidly con?rm a substantial num-ber of candidate SNe,but we can search for peculiarities in the spectra that might indicate evolution of SNe Ia with redshift.Moreover,high-quality spec-tra allow us to measure the age of a SN:we have developed a method for automatically comparing the spectrum of a SN Ia with a library of spectra from many di?erent epochs in the development of SNe Ia(Riess et al.1997). Our technique also has great practical utility at the telescope:we can de-termine the age of a SN“on the?y,”within half an hour after obtaining its spectrum.This allows us to decide rapidly which SNe are best for subsequent photometric follow-up,and we immediately alert our collaborators elsewhere.

4.2Results

First,we note that the light curves of high-redshift SNe Ia are broader than those of nearby SNe Ia;the initial indications(Leibundgut et al.1996;Gold-haber et al.1997),based on small numbers of SNe Ia,are amply con?rmed with the larger samples(Goldhaber et al.2001).Quantitatively,the amount by which the light curves are“stretched”is consistent with a factor of1+z, as expected if redshifts are produced by the expansion of space rather than by “tired light”and other non-expansion hypotheses for the redshifts of objects at cosmological distances.[For non-standard cosmological interpretations of the SN Ia data,see Narlikar&Arp(1997)and Hoyle,Burbidge,&Narlikar (2000).]We also demonstrate this spectroscopically at the2σcon?dence level for a single object:the spectrum of SN1996bj(z=0.57)evolved more slowly than those of nearby SNe Ia,by a factor consistent with1+z(Riess et al. 1997).More recently,we have used observations of SN1997ex(z=0.36) at three epochs to conclusively verify the e?ects of time dilation:temporal changes in the spectra are slower than those of nearby SNe Ia by roughly the expected factor of1.36.Although one might be able to argue that something other than universal expansion could be the cause of the apparent stretching

The Accelerating Universe9 of SN Ia light curves at high redshifts,it is much more di?cult to attribute apparently slower evolution of spectral details to an unknown e?ect.

The formal value of?M derived from SNe Ia has changed with time. The SCP published the?rst result(Perlmutter et al.1995a),based on a single object,SN1992bi at z=0.458:?M=0.2±0.6±1.1(assuming that ?Λ=0).The SCP’s analysis of their?rst seven objects(Perlmutter et al. 1997)suggested a much larger value of?M=0.88±0.6(if?Λ=0)or ?M=0.94±0.3(if?total=1).Such a high-density universe seemed at odds with other,independent measurements of?M.However,with the subsequent inclusion of just one more object,SN1997ap at z=0.83(the highest known for a SN Ia at the time;Perlmutter et al.1998),their estimates were revised back down to?M=0.2±0.4if?Λ=0,and?M=0.6±0.2if?total=1;the apparent brightness of SN1997ap had been precisely measured with HST,so it substantially a?ected the best?ts.

Meanwhile,the HZT published(Garnavich et al.1998a)an analysis of four objects(three of them observed with HST),including SN1997ck at z=0.97,at that time a redshift record,although they cannot be absolutely certain that the object was a SN Ia because the spectrum is too poor.From these data,the HZT derived that?M=?0.1±0.5(assuming?Λ=0) and?M=0.35±0.3(assuming?total=1),inconsistent with the high?M initially found by Perlmutter et al.(1997)but consistent with the revised estimate in Perlmutter et al.(1998).An independent analysis of10SNe Ia using the“snapshot”distance method(with which conclusions are drawn from sparsely observed SNe Ia)gave quantitatively similar conclusions(Riess et al.1998a).However,none of these early data sets carried the statistical discriminating power to detect cosmic acceleration.

The SCP’s next results were announced at the1998January AAS meet-ing in Washington,DC.A press conference was scheduled,with the stated purpose of presenting and discussing the then-current evidence for a low-?M universe as published by Perlmutter et al.(1998;SCP)and Garnavich et al. (1998a;HZT).When showing the SCP’s Hubble diagram for SNe Ia,however, Perlmutter also pointed out tentative evidence for acceleration!He said that the conclusion was uncertain,and that the data were equally consistent with no acceleration;the systematic errors had not yet been adequately assessed. Essentially the same conclusion was given by the SCP in their talks at a conference on dark matter,near Los Angeles,in February1998(Goldhaber &Perlmutter1998).

Although it chose not to reveal them at the same1998January AAS meeting,the HZT already had similar,tentative evidence for acceleration in their own SN Ia data set.The HZT continued to perform numerous checks of their data analysis and interpretation,including fairly thorough consideration of various possible systematic e?ects.Unable to?nd any signi?cant problems, even with the possible systematic e?ects,the HZT reported detection of a nonzero value for?Λ(based on16high-z SNe Ia)at the Los Angeles dark

10Alexei V.Filippenko

matter conference in February 1998(Filippenko &Riess 1998),and soon thereafter submitted a formal paper that was published in September 1998(Riess et al.1998b).Their original Hubble diagram for the 10best-observed high-z SNe Ia is given in Figure 3.With the MLCS method applied to the full set of 16SNe Ia,the HZT’s formal results were ?M =0.24±0.10if ?total =1,or ?M =?0.35±0.18(unphysical)if ?Λ=0.If one demanded that ?M =0.2,then the best value for ?Λwas 0.66±0.21.These conclusions did not change signi?cantly when only the 10best-observed SNe Ia were used (Figure 3;?M =0.28±0.10if ?total =1).

m -M (m a g )

z ?(m -M ) (m a g )Figure 3(left):The upper panel shows the Hubble diagram for the low-z and high-z HZT SN Ia sample with MLCS distances;see Riess et al.(1998b).Overplotted are three world models:“low”and “high”?M with ?Λ=0,and the best ?t for a ?at universe (?M =0.28,?Λ=0.72).The bottom panel shows the di?erence between data and models from the ?M =0.20,?Λ=0prediction.Only the 10best-observed high-z SNe Ia are shown.The average di?erence between the data and the ?M =0.20,?Λ=0prediction is ～0.25mag.

Figure 4(right):The HZT’s combined constraints from SNe Ia (left)and the position of the ?rst acoustic peak of the cosmic microwave background (CMB)angular power spectrum,based on data available in mid-1998;see Garnavich et al.(1998b).The contours mark the 68.3%,95.4%,and 99.7%en-closed probability regions.Solid curves correspond to results from the MLCS method;dotted ones are from the ?m 15(B )method;all 16SNe Ia in Riess et al.(1998b)were used.

The Accelerating Universe11 Another important constraint on the cosmological parameters could be obtained from measurements of the angular scale of the?rst acoustic peak of the CMB(e.g.,Zaldarriaga,Spergel,&Seljak1997;Eisenstein,Hu,& Tegmark1998);the SN Ia and CMB techniques provide nearly complemen-tary information.A stunning result was already available by mid-1998from existing measurements(e.g.,Hancock et al.1998;Lineweaver&Barbosa 1998):the HZT’s analysis of the SN Ia data in Riess et al.(1998b)demon-strated that?M+?Λ=0.94±0.26(Figure4),when the SN and CMB constraints were combined(Garnavich et al.1998b;see also Lineweaver1998, Efstathiou et al.1999,and others).

Somewhat later(June1999),the SCP published almost identical results, implying an accelerating expansion of the Universe,based on an essentially independent set of42high-z SNe Ia(Perlmutter et al.1999).Their data, together with those of the HZT,are shown in Figure5,and the corresponding con?dence contours in the?Λvs.?M plane are given in Figure6.This incredible agreement suggested that neither group had made a large,simple blunder;if the result was wrong,the reason must be subtle.Had there been only one team working in this area,it is likely that far fewer astronomers and physicists throughout the world would have taken the result seriously.

Moreover,already in1998–1999there was tentative evidence that the “dark energy”driving the accelerated expansion was indeed consistent with the cosmological constant,Λ.IfΛdominates,then the equation of state of the dark energy should have an index w=?1,where the pressure(P)and density(ρ)are related according to w=P/(ρc2).Garnavich et al.(1998b) and Perlmutter et al.(1999)were able to set an interesting limit,w<～?0.60 at the95%con?dence level.However,more high-quality data at z≈0.5 are needed to narrow the allowed range,in order to test other proposed candidates for dark energy such as various forms of“quintessence”(e.g., Caldwell,Dav′e,&Steinhardt1998).

Although the CMB results appeared reasonably persuasive in1998–1999, one could argue that?uctuations on di?erent scales had been measured with di?erent instruments,and that suble systematic e?ects might lead to erro-neous conclusions.These fears were dispelled only1–2years later,when the more accurate and precise results of the BOOMERANG collaboration were announced(de Bernardis et al.2000,2002).Shortly thereafter the MAXIMA collaboration distributed their very similar?ndings(Hanany et al.2000;Balbi et al.2000;Netter?eld et al.2002;see also the TOCO,DASI,and many other measurements).Figure6illustrates that the CMB measurements tightly con-strain?total to be close to unity;we appear to live in a?at universe,in agree-ment with most in?ationary models for the early Universe!Combined with the SN Ia results,the evidence for nonzero?Λwas fairly strong.Making the argument even more compelling was the fact that various studies of clusters of galaxies(see summary by Bahcall et al.1999)showed that?M≈0.3, consistent with the results in Figures4and6.Thus,a“concordance cosmol-

12Alexei V.Filippenko

ogy”had emerged:?M ≈0.3,?Λ≈0.7—consistent with what had been suspected some years earlier by Ostriker &Steinhardt (1995;see also Carroll,Press,&Turner 1992).

-0.5W =0.3, W =0.0

z D i s t a n c e M o d u l u s (m -M ) (m -M ) - (m -M )Figure 5(left):As in Figure 3,but this time including both the HZT (Riess et al.1998b)and SCP (Perlmutter et al.1999)samples of low-redshift and high-redshift SNe Ia.Overplotted are three world models:?M =0.3and 1.0with ?Λ=0,and a ?at universe (?total =1.0)with ?Λ=0.7.The bottom panel shows the di?erence between data and models from the ?M =0.3,?Λ=0prediction.

Figure 6(right):The combined constraints from SNe Ia (see Figure 5)and the position of the ?rst acoustic peak of the CMB angular power spectrum,based on BOOMERANG and MAXIMA data.The contours mark the 68.3%,95.4%,and 99.7%enclosed probability regions determined from the SNe Ia.According to the CMB,?total ≈1.0.

Yet another piece of evidence for a nonzero value of Λwas provided by the Two-Degree Field Galaxy Redshift Survey (2dFGRS;Peacock et al.2001;Percival et al.2001;Efstathiou et al.2002).Combined with the CMB maps,their results are inconsistent with a universe dominated by gravitating dark matter.Again,the implication is that about 70%of the mass-energy density of the Universe consists of some sort of dark energy whose gravita-tional e?ect is repulsive.Very recently,results from the Wilkinson Microwave Anisotropy Prove (WMAP)appeared;together with the 2dFGRS constraints,they con?rm and re?ne the concordance cosmology (?M =0.27,?Λ=0.73,?baryon =0.044,H 0=71±4km s ?1Mpc ?1;Spergel et al.2003).

The dynamical age of the Universe can be calculated from the cosmolog-ical parameters.In an empty Universe with no cosmological constant,the

The Accelerating Universe13 dynamical age is simply the“Hubble time”t0(i.e.,the inverse of the Hubble constant);there is no deceleration.In the late-1990s,SNe Ia gave H0=65±7 km s?1Mpc?1,and a Hubble time of15.1±1.6Gyr.For a more complex cosmology,integrating the velocity of the expansion from the current epoch (z=0)to the beginning(z=∞)yields an expression for the dynamical age. As shown in detail by Riess et al.(1998b),by mid-1998the HZT had obtained

a value of14.2+1.0

?0.8Gyr(with H0=65)using the likely range for(?M,?Λ)

that they measured.(The precision was so high because their experiment was sensitive to roughly the di?erence between?M and?Λ,and the dynamical age also varies in approximately this way.)Including the systematic uncer-tainty of the Cepheid distance scale,which may be up to10%,a reasonable estimate of the dynamical age was14.2±1.7Gyr(Riess et al.1998b).Again, the SCP’s result was very similar(Perlmutter et al.1999),since it was based on nearly the same derived values for the cosmological parameters.The most recent results,reported by Tonry et al.(2003)and adopting H0=72±8km s?1Mpc?1,give a dynamical age of13.1±1.5Gyr for the Universe—again, in agreement with the WMAP result of13.7±0.2Gyr.

This expansion age is also consistent with ages determined from various other techniques such as the cooling of white dwarfs(Galactic disk>9.5 Gyr;Oswalt et al.1996),radioactive dating of stars via the thorium and europium abundances(15.2±3.7Gyr;Cowan et al.1997),and studies of globular clusters(10–15Gyr,depending on whether Hipparcos parallaxes of Cepheids are adopted;Gratton et al.1997;Chaboyer et al.1998).The ages of the oldest stars no longer seem to exceed the expansion age of the Universe; the long-standing“age crisis”has evidently been resolved.

5Discussion

Although the convergence of di?erent methods on the same answer is reassur-ing,and suggests that the concordance cosmology is correct,it is important to vigorously test each method to make sure it is not leading us astray.More-over,only through such detailed studies will the accuracy and precision of the methods improve,allowing us to eventually set better constraints on the equation of state parameter,w.Here I discuss the systematic e?ects that could adversely a?ect the SN Ia results.

High-redshift SNe Ia are observed to be dimmer than expected in an empty Universe(i.e.,?M=0)with no cosmological constant.At z≈0.5, where the SN Ia observations have their greatest leverage onΛ,the di?erence in apparent magnitude between an?M=0.3(?Λ=0)universe and a?at universe with?Λ=0.7is only about0.25mag.Thus,we need to?nd out if chemical abundances,stellar populations,selection bias,gravitational lensing, or grey dust can have an e?ect this large.Although both the HZT and SCP had considered many of these potential systematic e?ects in their original discovery papers(Riess et al.1998b;Perlmutter et al.1999),and had shown

14Alexei V.Filippenko

with reasonable con?dence that obvious ones were not greatly a?ecting their conclusions,if was of course possible that they were wrong,and that the data were being misinterpreted.

5.1Evolution

Perhaps the most obvious possible culprit is evolution of SNe Ia over cosmic time,due to changes in metallicity,progenitor mass,or some other factor. If the peak luminosity of SNe Ia were lower at high redshift,then the case for?Λ>0would weaken.Conversely,if the distant explosions are more powerful,then the case for acceleration strengthens.Theorists are not yet sure what the sign of the e?ect will be,if it is present at all;di?erent assumptions lead to di?erent conclusions(H¨o?ich et al.1998;Umeda et al.1999;Nomoto et al.2000;Yungelson&Livio2000).

Of course,it is extremely di?cult,if not e?ectively impossible,to obtain an accurate,independent measure of the peak luminosity of high-z SNe Ia, and hence to directly test for luminosity evolution.However,we can more easily determine whether other observable properties of low-z and high-z SNe Ia di?er.If they are all the same,it is more probable that the peak luminosity is constant as well—but if they di?er,then the peak luminosity might also be a?ected(e.g.,H¨o?ich et al.1998).Drell,Loredo,&Wasserman (2000),for example,argue that there are reasons to suspect evolution,because the average properties of existing samples of high-z and low-z SNe Ia seem to di?er(e.g.,the high-z SNe Ia are more uniform).

The local sample of SNe Ia displays a weak correlation between light curve shape(or peak luminosity)and host galaxy type,in the sense that the most luminous SNe Ia with the broadest light curves only occur in late-type galaxies.Both early-type and late-type galaxies provide hosts for dimmer SNe Ia with narrower light curves(Hamuy et al.1996a).The mean luminosity di?erence for SNe Ia in late-type and early-type galaxies is～0.3mag.In addition,the SN Ia rate per unit luminosity is almost twice as high in late-type galaxies as in early-type galaxies at the present epoch(Cappellaro et al.1997).These results may indicate an evolution of SNe Ia with progenitor age.Possibly relevant physical parameters are the mass,metallicity,and C/O ratio of the progenitor(H¨o?ich et al.1998).

We expect that the relation between light curve shape and peak luminosity that applies to the range of stellar populations and progenitor ages encoun-tered in the late-type and early-type hosts in our nearby sample should also be applicable to the range we encounter in our distant sample.In fact,the range of age for SN Ia progenitors in the nearby sample is likely to be larger than the change in mean progenitor age over the4–6Gyr lookback time to the high-z sample.Thus,to?rst order at least,our local sample should correct the distances for progenitor or age e?ects.

The Accelerating Universe 15350040004500500055006000

6500

Rest Wavelength (Angstroms)

R e l a t i v e F l u x SN 1992a (z=0.01)

SN 1994B (z=0.09)

SN 1995E (z=0.01)

SN 1998ai (z=0.49)

SN 1989B (z=0.01)

Figure 7(left):Spectral comparison (in f λ)of SN 1998ai (z =0.49;Keck spectrum)with low-redshift (z <0.1)SNe Ia at a similar age (～5days before maximum brightness),from Riess et al.(1998b).The spectra of the low-redshift SNe Ia were resampled and convolved with Gaussian noise to match the quality of the spectrum of SN 1998ai.Overall,the agreement in the spectra is excellent,tentatively suggesting that distant SNe Ia are physically similar to nearby SNe Ia.SN 1994B (z =0.09)di?ers the most from the others,and was included as a “decoy.”

Figure 8(right):Heavily smoothed spectra of two high-z SNe (SN 1999?at z =0.455and SN 1999fv at z =1.19;quite noisy below ～3500?A )are presented along with several low-z SN Ia spectra (SNe 1989B,1992A,and 1981B),a SN Ib spectrum (SN 1993J),and a SN Ic spectrum (SN 1994I);see Filippenko (1997)for a discussion of spectra of various types of SNe.The date of the spectra relative to B -band maximum is shown in parentheses after each object’s name.Speci?c features seen in SN 1999?and labeled with a letter are discussed by Coil et al.(2000).This comparison shows that the two high-z SNe are most likely SNe Ia.

We can place empirical constraints on the e?ect that a change in the progenitor age would have on our SN Ia distances by comparing subsamples of low-redshift SNe Ia believed to arise from old and young progenitors.In the nearby sample,the mean di?erence between the distances for the early-type hosts (8SNe Ia)and late-type hosts (19SNe Ia),at a given redshift,is 0.04±0.07mag from the MLCS method.This di?erence is consistent with zero.Even if the SN Ia progenitors evolved from one population at low redshift to the other at high redshift,we still would not explain the surplus in mean

16Alexei V.Filippenko

distance of0.25mag over the?Λ=0prediction.Moreover,in a major study of high-redshift SNe Ia as a function of galaxy morphology,the SCP found no clear di?erences(except for the amount of scatter;see§5.2)between the cosmological results obtained with SNe Ia in late-type and early-type galaxies (Sullivan et al.2003).

It is also reassuring that initial comparisons of high-z SN Ia spectra ap-pear remarkably similar to those observed at low redshift.For example,the spectral characteristics of SN1998ai(z=0.49)appear to be essentially in-distinguishable from those of normal low-z SNe Ia;see Figure7.In fact,the most obviously discrepant spectrum in this?gure is the second one from the top,that of SN1994B(z=0.09);it is intentionally included as a“decoy”that illustrates the degree to which even the spectra of nearby,relatively nor-mal SNe Ia can vary.Nevertheless,it is important to note that a dispersion in luminosity(perhaps0.2mag)exists even among the other,more normal SNe Ia shown in Figure7;thus,our spectra of SN1998ai and other high-z SNe Ia are not yet su?ciently good for independent,precise determinations of peak luminosity from spectral features(Nugent et al.1995).Many of them, however,are su?cient for ruling out other SN types(Figure8),or for identi-fying gross peculiarities such as those shown by SNe1991T and1991bg;see Coil et al.(2000).

We can help verify that the SNe at z≈0.5being used for cosmology do not belong to a subluminous population of SNe Ia by examining restframe I-band light curves.Normal,nearby SNe Ia show a pronounced second maximum in the I band about a month after the?rst maximum and typically about0.5 mag fainter(e.g.,Ford et al.1993;Suntze?1996).Subluminous SNe Ia,in contrast,do not show this second maximum,but rather follow a linear decline or show a muted second maximum(Filippenko et al.1992a).As discussed by Riess et al.(2000),tentative evidence for the second maximum is seen from the HZT’s existing J-band(restframe I-band)data on SN1999Q(z=0.46); see Figure10.Additional tests with spectra and near-infrared light curves are currently being conducted.

Another way of using light curves to test for possible evolution of SNe Ia is to see whether the rise time(from explosion to maximum brightness)is the same for high-redshift and low-redshift SNe Ia;a di?erence might indicate that the peak luminosities are also di?erent(H¨o?ich et al.1998).Riess et al.(1999c)measured the risetime of nearby SNe Ia,using data from KAIT, the Beijing Astronomical Observatory(BAO)SN search,and a few amateur astronomers.Though the exact value of the risetime is a function of peak luminosity,for typical low-redshift SNe Ia it is20.0±0.2days.Riess et al. (1999b)pointed out that this di?ers by5.8σfrom the preliminary risetime of 17.5±0.4days reported in conferences by the SCP(Goldhaber et al.1998a,b; Groom1998).However,more thorough analyses of the SCP data(Aldering, Knop,&Nugent2000;Goldhaber et al.2001)show that the high-redshift uncertainty of±0.4days that the SCP originally reported was much too small

The Accelerating Universe17 because it did not account for systematic e?ects.The revised discrepancy with the low-redshift risetime is about2σor less.Thus,the apparent di?erence in risetimes might be insigni?cant.Even if the di?erence is real,however,its relevance to the peak luminosity is unclear;the light curves may di?er only in the?rst few days after the explosion,and this could be caused by small variations in conditions near the outer part of the exploding white dwarf that are inconsequential at the peak.

Figure9:The MLCS?t(Riess et al.1998b;left panel)and the stretch method ?t(Perlmutter et al.1999;right panel)for SN2000cx.The MLCS?t is the worst we had ever seen through2000.For the stretch method?t,the solid line is the?t to all the data points from t=?8to32days,the dash-dotted line uses only the premaximum datapoints,and the dashed line only the postmaximum datapoints.The three?ts give very di?erent stretch factors. From Li et al.(2001a).

Although there are no clear signs that cosmic evolution of SNe Ia seriously compromises our results,it is wise to remain vigilant for possible problems.At low redshifts,for example,we already know that some SNe Ia don’t conform with the correlation between light curve shape and luminosity.SN2000cx in the S0galaxy NGC524,for example,has light curves that cannot be?t well by any of the?tting techniques currently available(Li et al.2001a;Filippenko 2003);see Figure9.Its late-time color is remarkably blue,inconsistent with the homogeneity described by Phillips et al.(1999).The spectral evolution of SN2000cx is peculiar as well:the photosphere appears to have remained hot for a long time,and both iron-peak and intermediate-mass elements move at very high velocities.An even more peculiar object is SN2002cx(Li et al. 2003;Filippenko2003).It is spectroscopically bizarre,with extremely low expansion velocities and almost no evidence for intermediate-mass elements. The nebular phase was reached incredibly soon after maximum brightness,

18Alexei V.Filippenko

despite the low velocity of the ejecta,suggesting that the ejected mass is small.SN2002cx was subluminous by～2mag at all optical wavelengths relative to normal SNe Ia,despite the early-time spectroscopic resemblance to the somewhat overluminous SN1991T.The R-band and I-band light curves of SN2002cx are completely unlike those of normal SNe Ia.No existing theoretical model successfully explains all observed aspects of SN2002cx.If there are more strange beasts like SNe2000cx and2002cx at high redshifts than at low redshifts,systematic errors may creep into the analysis of high-z SNe Ia.

5.2Extinction

Our SN Ia distances have the important advantage of including corrections for interstellar extinction occurring in the host galaxy and the Milky Way. Extinction corrections based on the relation between SN Ia colors and lumi-nosity improve distance precision for a sample of nearby SNe Ia that includes objects with substantial extinction(Riess et al.1996a);the scatter in the Hubble diagram is much reduced.Moreover,the consistency of the measured Hubble?ow from SNe Ia with late-type and early-type hosts(see§5.1)shows that the extinction corrections applied to dusty SNe Ia at low redshift do not alter the expansion rate from its value measured from SNe Ia in low-dust environments.

In practice,the high-redshift SNe Ia generally appear to su?er very little extinction;their B?V colors at maximum brightness are normal,suggesting little color excess due to reddening.The most detailed available study is that of the SCP(Sullivan et al.2003):they found that the scatter in the Hub-ble diagram is minimal for SNe Ia in early-type host galaxies,but increases for SNe Ia in late-type galaxies.Moreover,on average the SNe in late-type galaxies are slightly fainter(by0.14±0.09mag)than those in early-type galaxies.Finally,at peak brightness the colors of SNe Ia in late-type galaxies are marginally redder than those in early-type galaxies.Sullivan et al.(2003) conclude that extinction by dust in the host galaxies of SNe Ia is one of the major sources of scatter in the high-redshift Hubble diagram.By restricting their sample to SNe Ia in early-type host galaxies(presumably with minimal extinction),they obtain a very tight Hubble diagram that suggests a nonzero value for?Λat the5σcon?dence level,under the assumption that?total=1. In the absence of this assumption,SNe Ia in early-type hosts still imply that ?Λ>0at nearly the98%con?dence level.The results for?Λwith SNe Ia in late-type galaxies are quantitatively similar,but statistically less secure because of the larger scatter.

Riess,Press,&Kirshner(1996b)found indications that the Galactic ra-tios between selective absorption and color excess are similar for host galaxies in the nearby(z≤0.1)Hubble?ow.Yet,what if these ratios changed with lookback time(e.g.,Aguirre1999a)?Could an evolution in dust-grain size de-scending from ancestral interstellar“pebbles”at higher redshifts cause us to

The Accelerating Universe 19

underestimate the extinction?Large dust grains would not imprint the red-dening signature of typical interstellar extinction upon which our corrections necessarily rely.

However,viewing our SNe through such gray interstellar grains would also induce a dispersion in the derived https://www.sodocs.net/doc/7c6228056.html,ing the results of Hatano,Branch,&Deaton (1998),Riess et al.(1998b)estimate that the expected dispersion would be 0.40mag if the mean gray extinction were 0.25mag (the value required to explain the measured MLCS distances without a cosmo-logical constant).This is signi?cantly larger than the 0.21mag dispersion observed in the high-redshift MLCS distances.Furthermore,most of the ob-served scatter is already consistent with the estimated statistical errors,leav-ing little to be caused by gray extinction.Nevertheless,if we assumed that all of the observed scatter were due to gray extinction,the mean shift in the SN Ia distances would be only 0.05mag.With the existing observations,it is di?cult to rule out this modest amount of gray interstellar extinction.

Time (relative to B maximum, days)r e l a t i v e I (m a g )

B -I (m a g )Age (days)E B -I (m a g )Figure 10(left):Restframe I -band (observed J -band)light curve of SN 1999Q (z =0.46,5solid points;Riess et al.2000),and the I -band light curves of several nearby SNe Ia.Subluminous SNe Ia exhibit a less prominent second maximum than do normal SNe Ia.

Figure 11(right):Color excess,E B ?I ,for SN 1999Q and di?erent dust models (Riess et al.2000).The data are most consistent with no dust and ?Λ>0.

Gray intergalactic extinction could dim the SNe without either telltale reddening or dispersion,if all lines of sight to a given redshift had a similar column density of absorbing material.The component of the intergalactic medium with such uniform coverage corresponds to the gas clouds producing Lyman-αforest absorption at low redshifts.These clouds have individual H I column densities less than about 1015cm ?2(Bahcall et al.1996).However,they display low metallicities,typically less than 10%of solar.Gray extinction

20Alexei V.Filippenko

would require larger dust grains which would need a larger mass in heavy elements than typical interstellar grain size distributions to achieve a given extinction.It is possible that large dust grains are blown out of galaxies by radiation pressure,and are therefore not associated with Lyman-αclouds (Aguirre1999b).

But even the dust postulated by Aguirre(1999a,b)and Aguirre&Haiman (1999)is not completely gray,having a size of about0.1μm.We can test for such nearly gray dust by observing high-redshift SNe Ia over a wide wave-length range to measure the color excess it would introduce.If A V=0.25 mag,then E(U?I)and E(B?I)should be0.12–0.16mag(Aguirre1999a,b). If,on the other hand,the0.25mag faintness is due toΛ,then no such red-dening should be seen.This e?ect is measurable using proven techniques;so far,with just one SN Ia(SN1999Q;Figure11),our results favor the no-dust hypothesis to better than2σ(Riess et al.2000).More work along these lines is in progress.

5.3The Smoking Gun

Suppose,however,that for some reason the dust is very gray,or our color measurements are not su?ciently precise to rule out Aguirre’s(or other)dust. Or,perhaps some other astrophysical systematic e?ect is fooling us,such as possible evolution of the white dwarf progenitors(e.g.,H¨o?ich et al.1998; Umeda et al.1999),or gravitational lensing(Wambsganss,Cen,&Ostriker 1998).The most decisive test to distinguish betweenΛand cumulative sys-tematic e?ects is to examine the deviation of the observed peak magnitude of SNe Ia from the magnitude expected in the low-?M,zero-Λmodel.IfΛis positive,the deviation should actually begin to decrease at z≈1;we will be looking so far back in time that theΛe?ect becomes small compared with ?M,and the Universe is decelerating at that epoch.If,on the other hand,a systematic bias such as gray dust or evolution of the white dwarf progenitors is the culprit,we expect that the deviation of the apparent magnitude will continue growing,unless the systematic bias is set up in such an unlikely way as to mimic the e?ects ofΛ(Drell et al.2000).A turnover,or decrease of the deviation of apparent magnitude at high redshift,can be considered the “smoking gun”ofΛ.

In a wonderful demonstration of good luck and hard work,Riess et al. (2001)report on HST observations of a probable SN Ia at z≈1.7(SN1997?, the most distant SN ever observed)that suggest the expected turnover is indeed present,providing a tantalizing glimpse of the epoch of deceleration. (See also Ben′?tez et al.2002,which corrects the observed magnitude of SN 1997?for gravitational lensing.)SN1997?was discovered by Gilliland& Phillips(1998)in a repeat HST observation of the Hubble Deep Field–North, and serendipitously monitored in the infrared with HST/NICMOS.The peak apparent SN brightness is consistent with that expected in the decelerating phase of the concordance cosmological model,?M≈0.3,?Λ≈0.7(Figure