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Arxiv:astro-ph/0303428v1 18 mar 2003

Measuring cosmology with Supernovae Saul Perlmutter1 and Brian P. Schmidt2 Physics Division, Lawrence Berkeley National Laboratory, University of California,Berkeley, CA 94720, USA Research School of Astronomy and Astrophysics, The Australian NationalUniversity, via Cotter Rd, Weston Creek, ACT 2611, Australia Abstract. Over the past decade, supernovae have emerged as some of the most power-ful tools for measuring extragalactic distances. A well developed physical understandingof type II supernovae allow them to be used to measure distances independent of theextragalactic distance scale. Type Ia supernovae are empirical tools whose precision andintrinsic brightness make them sensitive probes of the cosmological expansion. Bothtypes of supernovae are consistent with a Hubble Constant within ∼10% of H0 = 70 km s−1 Mpc−1. Two teams have used type Ia supernovae to trace the expansion of the Universe to a look-back time more than 60% of the age of the Universe. These observa-tions show an accelerating Universe which is currently best explained by a cosmologicalconstant or other form of dark energy with an equation of state near w = p/ρ = −1.
While there are many possible remaining systematic effects, none appears large enoughto challenge these current results. Future experiments are planned to better charac-terize the equation of state of the dark energy leading to the observed accelerationby observing hundreds or even thousands of objects. These experiments will need tocarefully control systematic errors to ensure future conclusions are not dominated byeffects unrelated to cosmology.
Understanding the global history of the Universe is a fundamental goal of cosmol-ogy. One of the conceptually simplest tests in the repertoire of the cosmologist isobserving how a standard candle dims as a function of redshift. The nearby Uni-verse provides the current rate of expansion, and with more distant objects it ispossible to start seeing the varied effects of cosmic curvature and the Universe's expansion history (usually expressed as the rate of acceleration/deceleration).
Over the past several decades a paradigm for understanding the global propertiesof the Universe has emerged based on General Relativity with the assumption ofa homogeneous and isotropic Universe. The relevant constants in this model arethe Hubble constant (or current rate of cosmic expansion), the relative fractionsof species of matter that contribute to the energy density of the Universe, andthese species' equation of state.
Early luminosity distance investigations used the brightest objects available for measuring distance – bright galaxies [3,39], but these efforts were hamperedby the impreciseness of the distance indicators and the changing properties ofthe distance indicators as a function of look back time. Although many othermethods for measuring the global curvature and cosmic deceleration exist (see, Perlmutter and Schmidt e.g., [66]), supernovae (SNe) have emerged as one of the preeminent distancemethods due to their significant intrinsic brightness (which allows them to beobservable in the distant Universe), ubiquity (they are visible in both the nearbyand distant Universe), and their precision (type Ia SNe provide distances thathave a precision of approximately 8%).
Supernovae as Distance Indicators Type II Supernovae and the Expanding Photosphere Method Massive stars come in a wide variety of luminosities and sizes and would seem-ingly not be useful objects for making distance measurements under the standardcandle assumption. However, from a radiative transfer standpoint these objectsare relatively simple and can be modeled with sufficient accuracy to measure dis-tances to approximately 10%. The expanding photosphere method (EPM), wasdeveloped by Kirshner and Kwan [44], and implemented on a large number ofobjects by Schmidt et al. [86] after considerable improvement in the theoreticalunderstanding of type II SN (SNII) atmospheres [15,16,99].
EPM assumes that SNII radiate as dilute blackbodies where θph is the angular size of the photosphere of the SN, Rph is the radius ofthe photosphere, D is the distance to the SN, Fλ is the observed flux density ofthe SN, and Bλ(T ) is the Planck function at a temperature T . Since SNII arenot perfect blackbodies, we include a correction factor, ζ, which is calculatedfrom radiate transfer models of SNII. SNe freely expand, and Rph = vph(t − t0) + R0, where vph is the observed velocity of material at the position of the photosphere,and t is the time elapsed since the time of explosion, t0. For most stars, the stellarradius ,R0, at the time of explosion is negligible, and Eqs. (1–2) can be combinedto yield By observing a SNII at several epochs, measuring the flux density and tem- perature of the SN (via broad band photometry) and vph from the minima ofthe weakest lines in the SN spectrum, we can solve simultaneously for the timeof explosion and distance to the SNII. The key to successfully measuring dis-tances via EPM is an accurate calculation of ζ(T ). Requisite calculations wereperformed by Eastman et al. [16] but, unfortunately, no other calculations ofζ(T ) have yet been published for typical SNIIP progenitors.
Measuring cosmology with Supernovae Hamuy et al. [34] and Leonard et al. [52] have measured the distances to SN1999em, and they have investigated other aspects of EPM. Hamuy et al. [34]challenged the prescription of measuring velocities from the minima of weaklines and developed a framework of cross correlating spectra with synthesizedspectra to estimate the velocity of material at the photosphere. This differentprescription does lead to small systematic differences in estimated velocity usingweak lines but, provided the modeled spectra are good representations of realobjects, this method should be more correct. At present, a revision of the EPMdistance scale using this method of estimating vph has not been made.
Leonard et al. [51] have obtained spectropolarimetry of SN1999em at many epochs and see polarization intrinsic to the SN which is consistent with the SNhave asymmetries of 10 − 20%. Asymmetries at this level are found in most SNII[101], and may ultimately limit the accuracy EPM can achieve on a single object(σ ∼ 10%). However, the mean of all SNII distances should remain unbiased.
Type II SNe have played an important role in measuring the Hubble constant independent of the rest of the extragalactic distance scale. In the next decadeit is quite likely that surveys will begin to turn up significant numbers of theseobjects at z ∼ 0.5 and, therefore, the possibility exists that SNII will be able tomake a contribution to the measurement of cosmological parameters beyond theHubble Constant. Since SNII do not have the precision of the SNIa (next section)and are significantly harder to measure, they will not replace the SNIa but willremain an independent class of objects which have the potential to confirm theinteresting results that have emerged from the SNIa studies.
Type Ia Supernovae as Standardized Candles SNIa have been used as extragalactic distance indicators since Kowal [42] firstpublished his Hubble diagram (σ = 0.6 mag) for type I SNe. We now recognizethat the old type I SNe spectroscopic class is comprised of two distinct physicalentities: SNIb/c which are massive stars that undergo core collapse (or in somerare cases might undergo a thermonuclear detonation in their cores) after los-ing their hydrogen atmospheres, and SNIa which are most likely thermonuclearexplosions of white dwarfs. In the mid-1980s it was recognized that studies ofthe type I SN sample had been confused by these similar appearing SNe, whichwere henceforth classified as type Ib [59,94,102] and type Ic [36]. By the late1980s/early 1990s, a strong case was being made that the vast majority of thetrue type Ia SNe had strikingly similar light curve shapes [11,46–48], spectraltime series [6,18,28,62], and absolute magnitudes [47,54]. There were a smallminority of clearly peculiar type Ia SNe (e.g., SN1986G [63], SN1991bg [19,49],and SN1991T [19,78]), but these could be identified and removed by their un-usual spectral features. A 1992 review by Branch and Tammann [7] of a varietyof studies in the literature concluded that the intrinsic dispersion in B and Vmaximum for type Ia SNe must be < 0.25 mag, making them "the best standardcandles known so far." In fact, the Branch and Tammann review indicated that the magnitude dis- persion was probably even smaller, but the measurement uncertainties in the Perlmutter and Schmidt available datasets were too large to tell. The Calan/Tololo Supernova Search(CTSS), a program begun by Hamuy et al. [31] in 1990, took the field a dra-matic step forward by obtaining a crucial set of high quality SN light curvesand spectra. By targeting a magnitude range that would discover type Ia SNein the redshift range z = 0.01 − 0.1, the CTSS was able to compare the peakmagnitudes of SNe whose relative distance could be deduced from their Hubblevelocities.
The CTSS observed some 25 fields (out of a total sample of 45 fields) twice a month for over three and one half years with photographic plates or film atthe Cerro Tololo Inter-American Observatory (CTIO) Curtis Schmidt telescope,and then organized extensive follow-up photometry campaigns primarily on theCTIO 0.9 m telescope, and spectroscopic observation on either the CTIO 4 mor 1.5 m telescope. Toward the end of this search, Hamuy et al. [31] pointedout the difficulty of this comprehensive project: "Unfortunately, the appearanceof a SN is not predictable. As a consequence of this we cannot schedule thefollowup observations a priori, and we generally have to rely on someone else'stelescope time. This makes the execution of this project somewhat difficult."Despite these challenges, the search was a major success; with the cooperationof many visiting CTIO astronomers and CTIO staff, it contributed 30 new typeIa SN light curves to the pool [32] with an almost unprecedented control ofmeasurement uncertainties.
As the CTSS data began to become available, several methods were presented that could select for the "most standard" subset of the type Ia standard candles,a subset which remained the dominant majority of the ever-growing sample [8].
For example, Vaughan et al. [97] presented a cut on the B-V color at maximumthat would select what were later called the "Branch Normal" SNIa, with anobserved dispersion of less than 0.25 mag.
Phillips [64] found a tight correlation between the rate at which a type Ia SN's luminosity declines and its absolute magnitude, a relation which apparentlyapplied not only to the Branch Normal type Ia SNe, but also to the peculiar typeIa SNe. Phillips plotted the absolute magnitude of the existing set of nearbySNIa, which had dense photoelectric or CCD coverage, versus the parameter∆m15(B), the amount the SN decreased in brightness in the B-band over the 15days following maximum light. The sample showed a strong correlation which,if removed, dramatically improved the predictive power of SNIa. Hamuy et al.
[33] used this empirical relation to reduce the scatter in the Hubble diagram toσ < 0.2 mag in V for a sample of nearly 30 SNIa from the CTSS search.
Impressed by the success of the ∆m15(B) parameter, Riess et al. [79] devel- oped the multi-color light curve shape method (MLCS), which parameterized theshape of SN light curves as a function of their absolute magnitude at maximum.
This method also included a sophisticated error model and fitted observationsin all colors simultaneously, allowing a color excess to be included. This colorexcess, which we attribute to intervening dust, enabled the extinction to be mea-sured. Another method that has been used widely in cosmological measurementswith SNIa is the "stretch" method described in Perlmutter et al. [74,77]. This Measuring cosmology with Supernovae method is based on the observation that the entire range of SNIa light curves,at least in the B and V-bands, can be represented with a simple time stretching(or shrinking) of a canonical light curve. The coupled stretched B and V lightcurves serve as a parameterized set of light curve shapes [26], providing manyof the benefits of the MLCS method but as a much simpler (and constrained)set. This method, as well as recent implementations of ∆m15(B) [24,65], alsoallows extinction to be directly incorporated into the SNIa distance measure-ments. Other methods that correct for intrinsic luminosity differences or limitthe input sample by various criteria have also been proposed to increase theprecision of type Ia SNe as distance indicators [9,17,93,95]. While these lattertechniques are not as developed as the ∆m15(B), MLCS, and stretch methods,they all provide distances that are comparable in precision, roughly σ = 0.18mag about the inverse square law, equating to a fundamental precision of SNIadistances of ∼ 6% (0.12 mag), once photometric uncertainties and peculiar ve-locities are removed. Finally, a "poor man's" distance indicator, the snapshotmethod [80], combines information contained in one or more SN spectra withas little as one night's multi-color photometry. This method's accuracy dependscritically on how much information is available.
Cosmological Parameters The standard model for describing the global evolution of the Universe is basedon two equations that make some simple, and hopefully valid, assumptions. Ifthe Universe is isotropic and homogenous on large scales, the Robertson-WalkerMetric, ds2 = dt2 − a(t) gives the line element distance(s) between two objects with coordinates r,θ andtime separation, t. The Universe is assumed to have a simple topology suchthat, if it has negative, zero, or positive curvature, k takes the value −1, 0, 1,respectively. These models of the Universe are said to be open, flat, or closed,respectively. The dynamic evolution of the Universe needs to be input into theRobertson-Walker Metric by the specification of the scale factor a(t), which givesthe radius of curvature of the Universe over time – or more simply, provides therelative size of a piece of space at any time. This description of the dynamics ofthe Universe is derived from General Relativity, and is known as the Friedmanequation H2 ≡ ( ˙a/a)2 = The expansion rate of our Universe (H), is called the Hubble parameter (or the Hubble constant, H0, at the present epoch) and depends on the content ofthe Universe. Here we assume the Universe is composed of a set of components,each having a fraction, Ωi, of the critical density Perlmutter and Schmidt with an equation of state which relates the density, ρi, and pressure, pi, as wi =pi/ρi. For example, wi takes the value 0 for normal matter, +1/3 for photons,and -1 for the cosmological constant. The equation of state parameter does notneed to remain fixed; if scalar fields are present, the effective w will change overtime. Most reasonable forms of matter or scalar fields have wi ≥ −1, althoughnothing seems manifestly forbidden. Combining Eqs. (4–6) yields solutions tothe global evolution of the Universe [13].
The luminosity distance, DL, which is defined as the apparent brightness of an object as a function of its redshift z – the amount an object's light hasbeen stretched by the expansion of the Universe – can be derived from Eqs. (4–6) by solving for the surface area as a function of z, and taking into accountthe effects of time dilation [25,26,50,82] and energy dimunition as photons getstretched traveling through the expanding Universe. DL is given by the numer-ically integrable equation, (1 + z)κ−1/2S{κ1/2 i(1 + z")3+3wi − κ0(1 + z")2]−1/2}. (7) S(x) = sin(x), x, or sinh(x) for closed, flat, and open models respectively, andthe curvature parameter κ0, is defined as κ0 = ( Ω Historically, Eq. (7) has not been easily integrated and has been expanded in a Taylor series to give where the deceleration parameter, q0, is given by From Eq. (9) we can see that, in the nearby Universe, the luminosity distances scale linearly with redshift, with H0 serving as the constant of proportionality.
In the more distant Universe, DL depends to first order on the rate of accel-eration/deceleration (q0) or, equivalently, on the amount and types of matterthat make up the Universe. For example, since normal matter has wM = 0 andthe cosmological constant has wΛ = −1, a universe composed of only these twoforms of matter/energy has q0 = ΩM /2 − ΩΛ. In a universe composed of thesetwo types of matter, if ΩΛ < ΩM /2, q0 is positive and the universe is decelerat-ing. These decelerating universes have DL smaller as a function of z than theiraccelerating counterparts.
If distance measurements are made at a low-z and a small range of redshift at higher z (e.g., 0.3 > z > 0.5), there is a degeneracy between ΩM and ΩΛ.
Measuring cosmology with Supernovae DL expressed as distance modulus (m − M ) for four relevant cosmological models; ΩM = 0, ΩΛ = 0 (empty Universe, solid line); ΩM = 0.3, ΩΛ = 0 (shortdashed line); ΩM = 0.3, ΩΛ = 0.7 (hatched line); and ΩM = 1.0, ΩΛ = 0 (long dashedline). In the bottom panel the empty Universe has been subtracted from the othermodels to highlight the differences.
It is impossible to pin down the absolute amount of either species of matter.
One can only determine their relative dominance, which, at z = 0, is given byEq. (9). However, Goobar and Perlmutter [27] pointed out that by observingobjects over a larger range of high redshift (e.g., 0.3 > z > 1.0) this degeneracycan be broken, providing a measurement of the absolute fractions of ΩM andΩΛ.
To illustrate the effect of cosmological parameters on the luminosity distance, in Fig. 1 we plot a series of models for both Λ and non-Λ universes. In the top Perlmutter and Schmidt Fig. 2. DL for a variety of cosmological models containing ΩM = 0.3 and Ωx = 0.7with a constant (not time-varying) equation of state wx. The wx = −1 model has beensubtracted off to highlight the differences between the various models panel, the various models show the same linear behavior at z < 0.1 with modelshaving the same H0 being indistinguishable to a few percent. By z = 0.5 themodels with significant Λ are clearly separated, with luminosity distances thatare significantly further than the zero-Λ universes. Unfortunately, two perfectlyreasonable universes, given our knowledge of the local matter density of theUniverse (ΩM ∼ 0.2), one with a large cosmological constant, ΩΛ = 0.7, ΩM =0.3 and one with no cosmological constant, ΩM = 0.2, show differences of lessthan 25%, even to redshifts of z > 5. Interestingly, the maximum differencebetween the two models is at z ∼ 0.8, not at large z. Fig. 2 illustrates the effect Measuring cosmology with Supernovae of changing the equation of state of the non-matter, dark energy component,assuming a flat universe, Ωtot = 1. If we are to discern a dark energy componentthat is not a cosmological constant, measurements better than 5% are clearlyrequired, especially since the differences in this diagram include the assumptionof flatness and also fix the value of ΩM . In fact, to discriminate among the fullrange of dark energy models with time varying equations of state will requiremuch better accuracy than even this challenging goal.
Measuring the Hubble Constant Schmidt et al. [86], using a sample of 16 SNII, estimated H0 = 73±6(statistical)±7(systematic) using EPM. This estimate is independent of other rungs in the ex-tragalactic distance ladder, the most important of which are the Cepheids, whichcurrently calibrate most other distance methods (such as SNIa). The Cepheidand EPM distance scales, compared galaxy to galaxy, agree to within 5% and areconsistent within the errors [16,52]. This provides confidence that both methodsare providing accurate distances.
The current nearby SNIa sample [24,32,41,84] contains more than 100 objects (Fig. 3), and accurately defines the slope in the Hubble diagram from 0 < z < 0.1to 1%. To measure H0, SNIa must still be externally calibrated with Cepheids,and this calibration is the major limitation to measuring H0 with SNIa. Twoseparate teams have analyzed the Cepheids and SNIa but have obtained di-vergent values for the Hubble constant. Saha et al. [88] find H0 = 59 ± 6,whereas Freedman et al. [20] find H0 = 71 ± 2 ± (6 systematic). Of the 12SNIa for which there are Cepheid distances to the host galaxy (SN1895B∗,SN1937C∗, SN1960F∗, SN1972E, SN1974G∗, SN1981B, SN1989B, SN1990N,SN1991T, SN1998eq, SN1998bu, and SN1999by), four were observed by non-digital means (marked by ∗) and are best excluded from analysis on the groundsthat non-digital photometry routinely has systematic errors far greater than 0.1mag. Jha [41] has compared the SNIa distances using an updated version ofMLCS to the Cepheid host galaxy distances measured by the two Hubble SpaceTelescope (HST) teams. Using only the digitally observed SNIa, he finds, usingdistances from the SNIa project of Saha et al. [88], H0 = 66 ± 3 ± (7 systematic) km s−1 Mpc−1. Applying the same analysis to the Key Project distances by Freedman et al. [20] gives H0 = 76 ± 3 ± (8 systematic) km s−1 Mpc−1. Thisdifference is not due to SNIa errors, but rather to the different ways the twoteams have measured Cepheid distances with HST. The two values do overlapwhen the systematic uncertainties are included, but it is still uncomfortable thatthe discrepancies are so large, particularly when some systematic uncertaintiesare common between the two teams.
At present, SNe provide the most convincing constraints with H0 ∼ 70 ± 10 km s−1 Mpc−1. However, future work on measuring H0 lies not with the SNe but with the Cepheid calibrators, or possibly in using other primary distanceindicators such as EPM or the Sunyaev-Zeldovich effect.
Perlmutter and Schmidt Fig. 3. The Hubble diagram for SNIa from 0.01 > z > 0.2 [24,33,41,84]. The 102objects in this range have a residual about the inverse square line of ∼ 10%.
The Measurement of Acceleration The intrinsic brightness of SNIa allow them to be discovered to z > 1.5 withcurrent instrumentation (while a comparably deep search for type II SNe wouldonly reach redshifts of z ∼ 0.5). In the 1980s, however, finding, identifying, andstudying even the impressively luminous type Ia SNe was a daunting challenge,even towards the lower end of the redshift range shown in Fig. 1. At theseredshifts, beyond z ∼ 0.25, Fig. 1 shows that relevant cosmological models couldbe distinguished by differences of order 0.2 mag in their predicted luminositydistances. For SNIa with a dispersion of 0.2 mag, 10 well observed objects shouldprovide a 3σ separation between the various cosmological models. It should benoted that the uncertainty described above in measuring H0 is not importantin measuring the parameters for different cosmological models. Only the relativebrightness of objects near and far is being exploited in Eq. (7) and the absolutevalue of H0 scales out.
The first distant SN search was started by the Danish team of Nørgaard- Nielsen et al. [57]. With significant effort and large amounts of telescope timespread over more than two years, they discovered a single SNIa in a z = 0.3cluster of galaxies (and one SNII at z = 0.2) [35,57]. The SNIa was discoveredwell after maximum light on an observing night that could not have been pre-dicted, and was only marginally useful for cosmology. However, it showed that Measuring cosmology with Supernovae such high redshift SNe did exist and could be found, but that they would bevery difficult to use as cosmological tools.
Just before this first discovery in 1988, a search for high redshift type Ia SNe using a then novel wide field camera on a much larger (4m) telescope wasbegun at the Lawrence Berkeley National Laboratory (LBNL) and the Centerfor Particle Astrophysics, at Berkeley. This search, now known as the SupernovaCosmological Project (SCP), was inspired by the impressive studies of the late1980s indicating that extremely similar type Ia SN events could be recognizedby their spectra and light curves, and by the success of the LBNL fully roboticlow-redshift SN search in finding 20 SNe with automatic image analysis [56,67].
The SCP targeted a much higher redshift range, z > 0.3, in order to measure the (presumed) deceleration of the Universe, so it faced a different challengethan the CTSS search. The high redshift SNe required discovery, spectroscopicconfirmation, and photometric follow up on much larger telescopes. This precioustelescope time could neither be borrowed from other visiting observers and staffnor applied for in sufficient quantities spread throughout the year to cover allSNe discovered in a given search field, and with observations early enough toestablish their peak brightness. Moreover, since the observing time to confirmhigh redshift SNe was significant on the largest telescopes, there was a clear"chicken and egg" problem: telescope time assignment committees would notaward follow-up time for a SN discovery that might, or might not, happen on agiven run (and might, or might not, be well past maximum) and, without thefollow-up time, it was impossible to demonstrate that high redshift SNe werebeing discovered by the SCP.
By 1994, the SCP had solved this problem, first by providing convincing ev- idence that SNe, such as SN1992bi, could be discovered near maximum (andK-corrected) out to z = 0.45 [73], and then by developing and successfullydemonstrating a new observing strategy that could effectively guarantee SN dis-coveries on a predetermined date, all before or near maximum light [70–72,76].
Instead of discovering a single SN at a time on average (with some runs notfinding one at all), the new approach aimed to discover an entire "batch" ofhalf-a-dozen or more type Ia SNe at a time by observing a much larger numberof galaxies in a single two or three day period a few nights before new Moon. Bycomparing these observations with the same observations taken towards the endof dark time almost three weeks earlier, it was possible to select just those SNethat were still on the rise or near maximum. The chicken and egg problem wassolved, and now the follow-up spectroscopy and photometry could be appliedfor and scheduled on a pre-specified set of nights. The new strategy worked –the SCP discovered batches of high redshift SNe,and no one would ever againhave to hunt for high-redshift SNe without the crucial follow-up scheduled inadvance.
The High-Z SN Search (HZSNS) was conceived at the end of 1994, when this group of astronomers became convinced that it was both possible to discoverSNIa in large numbers at z > 0.3 by the efforts of Perlmutter et al.[70–72], andalso use them as precision distance indicators as demonstrated by the CTSS Perlmutter and Schmidt group [32]. Since 1995, the SCP and HZSNS have both worked avidly to obtaina significant set of high redshift SNIa.
The two high redshift teams both used this pre-scheduled discovery and follow-up batch strategy. They each aimed to use the observing resources they hadavailable to best scientific advantage, choosing, for example, somewhat differentexposure times or filters.
Quantitatively, type Ia SNe are rare events on an astronomer's time scale – they occur in a galaxy like the Milky Way a few times per millennium (see,e.g., [12,60,61] and the chapter by Cappellaro in this volume). With moderninstruments on 4 meter-class telescopes, which observe 1/3 of a square degree toR = 24 mag in less than 10 minutes, it is possible to search a million galaxies toz < 0.5 for SNIa in a single night.
Since SNIa take approximately 20 days to rise from undetectable to max- imum light [81], the three-week separation between observing periods (whichequates to 14 rest frame days at z = 0.5) is a good filter to catch the SNe onthe rise. The SNe are not always easily identified as new stars on the brightbackground of their host galaxies, so a relatively sophisticated process must beused to identify them. The process, which involves 20 Gigabytes of imaging dataper night, consists of aligning a previous epoch, matching the image star profiles(through convolution), and scaling the two epochs to make the two images asidentical as possible. The difference between these two images is then searchedfor new objects which stand out against the static sources that have been largelyremoved in the differencing process [73,74,76,87]. The dramatic increase in com-puting power in the 1980s was an important element in the development of thissearch technique, as was the construction of wide-field cameras with ever largerCCD detectors or mosaics of such detectors [104].
This technique is very efficient at producing large numbers of objects that are, on average, at or near maximum light, and does not require unrealisticamounts of large telescope time. It does, however, place the burden of work onfollow-up observations, usually with different instruments on different telescopes.
With the large number of objects discovered (50 in two nights being typical),a new strategy is being adopted by both the SCP and HZSNS teams, as wellas additional teams like the Canada France Hawaii Telescope (CFHT) legacysurvey, where the same fields are repeatedly scanned several times per month, inmultiple colors, for several consecutive months. This type of observing programprovides both discovery of new objects and their follow up, all integrated into oneefficient program. It does require a large block of time on a single telescope – arequirement which was not politically feasible in years past, but is now possible.
Obstacles to Measuring Luminosity Distances at High-Z As shown above, the distances measured to SNIa are well characterized at z <0.1, but comparing these objects to their more distant counterparts requires great Measuring cosmology with Supernovae care. Selection effects can introduce systematic errors as a function of redshift,as can uncertain K-corrections and a possible evolution of the SNIa progenitorpopulation as a function of look-back time. These effects, if they are large andnot constrained or corrected, will limit our ability to accurately measure relativeluminosity distances, and have the potential to reduce the efficacy of high-z typeIa SNe for measuring cosmology [74,77,83,87].
K-Corrections: As SNe are observed at larger and larger redshifts, their lightis shifted to longer wavelengths. Since astronomical observations are normallymade in fixed band passes on Earth, corrections need to be applied to account forthe differences caused by the spectrum shifting within these band passes. Thesecorrections take the form of integrating the spectrum of an SN over the relevantband passes, shifting the SN spectrum to the correct redshift, and re-integrating.
Kim et al. [43] showed that these effects can be minimized if one does not usea single bandpass, but instead chooses the bandpass closest to the redshiftedrest-frame bandpass, as they had done for SN1992bi [73]. They showed that theinter-band K-correction is given by ij (z) = 2.5 log (1 + z) ) F (λ/(1 + z))S where Kij(z) is the correction to go from filter i to filter j, and Z(λ) is thespectrum corresponding to zero magnitude of the filters.
The brightness of an object expressed in magnitudes, as a function of z is where DL(z) is given by Eq. (7), Mj is the absolute magnitude of object infilter j, and Kij is given by Eq. (10). For example, for H0 = 70 km s−1 Mpc−1,and DL = 2835 Mpc (ΩM = 0.3, ΩΛ = 0.7), at maximum light a SNIa hasMB = −19.5 mag and a KBR = −0.7 mag. We therefore expect an SNIa atz = 0.5 to peak at mR ∼ 22.1 mag for this set of cosmological parameters.
K-correction errors depend critically on three uncertainties: 1. Accuracy of spectrophotometry of SNe. To calculate the K-correction, the spectra of SNe are integrated in Eq. (10). These integrals are insensitiveto a grey shift in the flux calibration of the spectra, but any wavelengthdependent flux calibration error will translate into erroneous K-corrections.
2. Accuracy of the absolute calibration of the fundamental astronomical stan- dard systems. Eq. (10) shows that the K-corrections are sensitive to theshape of the astronomical band passes and to the zero points of these bandpasses.
3. Accuracy of the choice of SNIa spectrophotometry template used to calculate the corrections. Although a relatively homogenous class, there are variationsin the spectra of SNIa. If a particular object has, for example, a stronger Perlmutter and Schmidt calcium triplet than the average SNIa, the K-corrections will be in errorunless an appropriate subset of SNIa spectra are used in the calculations.
The first error should not be an issue if correct observational procedures are used on an instrument that has no fundamental problems. The second error iscurrently estimated to be small (∼ 0.01 mag), based on the consistency of spec-trophotometry and broadband photometry of the fundamental standards, Siriusand Vega [5]. To improve this uncertainty will require new, careful experimentsto accurately calibrate a star, such as Vega or Sirius (or a White Dwarf or solaranalog star), and to carefully infer the standard bandpass that defines the pho-tometric system in use at telescopes. The third error requires a large database tomatch as closely as possible an SN with the spectrophotometry used to calculatethe K-corrections. Nugent et al. [58] have shown that extinction and color arerelated and, by correcting the spectra to force them to match the photometryof the SN needing K-corrections, that it is possible to largely eliminate errors 1and 3, even when using spectra that are not exact matches (in epoch or in finedetail) to the SNIa being K-corrected. Scatter in the measured K-correctionsfrom a variety of telescopes and objects allows us to estimate the combined sizeof the effect for the first and third errors. These appear to be ∼ 0.01 mag forredshifts where the high-z and low-z filters have a large region of overlap (e.g.,R-band matched to B-band at z = 0.5).
Extinction: In the nearby Universe we see SNIa in a variety of environments,and about 10% have significant extinction [30]. Since we can correct for extinc-tion by observing two or more wavelengths, it is possible to remove any firstorder effects caused by a changing average extinction of SNIa as a function of z.
However, second order effects, such as possible evolution of the average proper-ties of intervening dust, could still introduce systematic errors. This problem canalso be addressed by observing distant SNIa over a decade or so of wavelengthin order to measure the extinction law to individual objects. Unfortunately, thisis observationally very expensive. Current observations limit the total system-atic effect to < 0.06 mag, as most of our current data is based on two colorobservations.
An additional problem is the existence of a thin veil of dust around the Milky Way. Measurements from the Cosmic Background Explorer (COBE) satelliteaccurately determined the relative amount of dust around the Galaxy [89], butthere is an uncertainty in the absolute amount of extinction of about 2 − 3%.
This uncertainty is not normally a problem, since it affects everything in the skymore or less equally. However, as we observe SNe at higher and higher redshifts,the light from the objects is shifted to the red and is less affected by the Galacticdust. Our present knowledge indicates that a systematic error as large as 0.06mag is attributable to this uncertainty.
Selection Effects: As we discover SNe, we are subject to a variety of selectioneffects, both in our nearby and distant searches. The most significant effect is the Measuring cosmology with Supernovae Malmquist Bias – a selection effect which leads magnitude limited searches tofind brighter than average objects near their distance limit since brighter objectscan be seen in a larger volume than their fainter counterparts. Malmquist Biaserrors are proportional to the square of the intrinsic dispersion of the distancemethod, and because SNIa are such accurate distance indicators these errors arequite small, ∼ 0.04 mag. Monte Carlo simulations can be used to estimate suchselection effects, and to remove them from our data sets [74,76,77,87]. The totaluncertainty from selection effects is ∼ 0.01 mag and, interestingly, may be worsefor lower redshift objects because they are, at present, more poorly quantified.
Gravitational Lensing: Several authors have pointed out that the radiationfrom any object, as it traverses the large scale structure between where it wasemitted and where it is detected, will be weakly lensed as it encounters fluctu-ations in the gravitational potential [37,45,100]. On average, most of the lighttravel paths go through under-dense regions and objects appear de-magnified.
Occasionally, the light path encounters dense regions and the object becomesmagnified. The distribution of observed fluxes for sources is skewed by this pro-cess such that the vast majority of objects appear slightly fainter than the canon-ical luminosity distance, with the few highly magnified events making the meanof all light paths unbiased. Unfortunately, since we do not observe enough ob-jects to capture the entire distribution, unless we know and include the skewedshape of the lensing a bias will occur. At z = 0.5, this lensing is not a significantproblem: If the Universe is flat in normal matter, the large scale structure caninduce a shift of the mode of the distribution by only a few percent. However,the effect scales roughly as z2, and by z = 1.5 the effect can be as large as 25%[38]. While corrections can be derived by measuring the distortion of backgroundgalaxies near the line of sight to each SN, at z > 1, this problem may be onewhich ultimately limits the accuracy of luminosity distance measurements, un-less a large enough sample of SNe at each redshift can be used to characterizethe lensing distribution and average out the effect. For the z ∼ 0.5 sample, theerror is < 0.02 mag, but it is much more significant at z > 1 (e.g., for SN1997ff)[4,55], especially if the sample size is small.
Evolution: SNIa are seen to evolve in the nearby Universe. Hamuy et al. [29]plotted the shape of the SN light curves against the type of host galaxy. SNein early hosts (galaxies without recent star formation) consistently show lightcurves which rise and fade more quickly than SNe in late-type hosts (galaxieswith on-going star formation). However, once corrected for light curve shape theluminosity shows no bias as a function of host type. This empirical investigationprovides reassurance for using SNIa as distance indicators over a variety of stel-lar population ages. It is possible, of course, to devise scenarios where some ofthe more distant SNe do not have nearby analogues, so as supernovae are stud-ied at increasingly higher redshifts it can become important to obtain detailedspectroscopic and photometric observations of every distant SN to recognize andreject examples that have no nearby analogues.
Perlmutter and Schmidt In principle, it should be possible to use differences in the spectra and light curves between nearby and distant SNe, combined with theoretical modeling, tocorrect any differences in absolute magnitude. Unfortunately, theoretical inves-tigations are not yet advanced enough to precisely quantify the effect of thesedifferences on the absolute magnitude. A different, empirical approach to handleSN evolution [10] is to divide the SNe into subsamples of very closely matchedevents, based on the details of the their light curves, spectral time series, hostgalaxy properties, etc. A separate Hubble diagram can then be constructed foreach subsample of SNe, and each will yield an independent measurement of thecosmological parameters. The agreement (or disagreement) between the resultsfrom the separate subsamples is an indicator of the total effect of evolution. Asimple, first attempt at this kind of test has been performed by comparing theresults for SNe found in elliptical host galaxies to SNe found in late spirals orirregular hosts, and the cosmological results from these subsamples were foundto agree well [91].
Finally, it is possible to move to higher redshifts and see if the SNe deviate from the predictions of Eq. (7). At a gross level, we expect an accelerating Uni-verse to be decelerating in the past because the matter density of the Universeincreases with redshift, whereas the density of any dark energy leading to ac-celeration will increase at a slower rate than this (or not at all in the case ofa cosmological constant). If the observed acceleration is caused by some sort ofsystematic effect, it is likely to continue to increase (or at least remain steady)with z, rather than disappear like the effects of dark energy. A first comparisonhas been made with SN1997ff at z ∼ 1.7 [85], and it seems consistent with adecelerating Universe at that epoch. More objects are necessary for a definitiveanswer, and these should be provided by several large programs that have beendiscovering such type Ia SNe at the W.M. Keck Telescope I (KECK I), SubaruTelescope), and HST telescopes.
High Redshift SNIa Observations The SCP [74] in 1997 presented their first results with 7 objects at a redshiftaround z = 0.4. These objects hinted at a decelerating Universe with a measure-ment of ΩM = 0.88+0.69, but were not definitive. Soon after, the SCP published a further result, with a z ∼ 0.84 SNIa observed with the KECK I and HSTadded to the sample [75], and the HZSNS presented the results from their firstfour objects [22,87]. The results from both teams now ruled out a ΩM = 1 Uni-verse with greater than 95% significance. These findings were again supercededdramatically when both teams announced results including more SNe (10 moreHZSNS SNe, and 34 more SCP SNe) that showed not only were the SN obser-vations incompatible with a ΩM = 1 Universe, they were also incompatible witha Universe containing only normal matter [77,83]. Fig. 4 shows the Hubble dia-gram for both teams. Both samples show that SNe are, on average, fainter thanwould be expected, even for an empty Universe, indicating that the Universe isaccelerating. The agreement between the experimental results of the two teams Measuring cosmology with Supernovae Fig. 4. Upper panel: The Hubble diagram for high redshift SNIa from both the HZSNS[83] and the SCP [77]. Lower panel: The residual of the distances relative to a ΩM = 0.3,ΩΛ = 0.7 Universe. The z < 0.15 objects for both teams are drawn from CTSS sample[32], so many of these objects are in common between the analyses of the two teams.
Perlmutter and Schmidt (cosmological constant) vacuum energy density recol apses eventual y Fig. 5. The confidence regions for both HZSNS [83] and SCP [77] for ΩM , ΩΛ. The twoexperiments show, with remarkable consistency, that ΩΛ > 0 is required to reconcileobservations and theory. The SCP result is based on measurements of 42 distant SNIa.
(The analysis shown here is uncorrected for host galaxy extinction;see [77] for thealternative analyses with host extinction correction, which is shown to make littledifference in this data set.) The HZSNS result is based on measurements of 16 SNIa,including 6 snapshot distances [80], of which two are SCP SNe from the 42 SN sample.
The z < 0.15 objects used to constrain the fit for both teams are drawn from the CTSSsample [32], so many of these objects are common between the analyses by the twoteams.
Measuring cosmology with Supernovae Fig. 6. Left panel: Contours of ΩM versus wx from current observational data. RightPanel: Contours of ΩM versus wx from current observational data, where the currentvalue of ΩM is obtained from the 2dF redshift survey. For both panels ΩM + Ωx = 1is taken as a prior.
is spectacular, especially considering the two programs have worked in almostcomplete isolation from each other.
The easiest solution to explain the observed acceleration is to include an ad- ditional component of matter with an equation of state parameter more negativethan w < −1/3; the most familiar being the cosmological constant (w = −1).
Fig. 5 shows the joint confidence contours for values of ΩM and ΩΛ from bothexperiments. If we assume the Universe is composed only of normal matter anda cosmological constant, then with greater than 99.9% confidence the Universehas a non-zero cosmological constant or some other form of dark energy.
Of course, we do not know the form of dark energy which is leading to the acceleration, and it is worthwhile investigating what other forms of energy arepossible additional components. Fig. 6 shows the joint confidence contours forthe HZSNS+SCP observations for ΩM and wx (the equation of state of theunknown component causing the acceleration). Because this introduces an extraparameter, we apply the additional constraint that ΩM +Ωx = 1, as indicated bythe CMB experiments [14]. The cosmological constant is preferred, but anythingwith a w < −0.5 is acceptable [23,77]. Additionally, we can add informationabout the value of ΩM , as supplied by recent 2dF redshift survey results [98], asshown in the 2nd panel, where the constraint strengthens to w < −0.6 at 95%confidence [69].
Perlmutter and Schmidt Marginalizing 200 high-redshift SN constant-w + 300 low-redshift SN 200 high-redshift SN + 300 low-redshift Fig. 7. Future expected constraints on dark energy: Left panel: Estimated 68% con-fidence regions for a constant equation of state parameter for the dark energy, w,versus mass density, for a ground-based study with 200 SNe between z = 0.3 − 0.7(open contours), and for the satellite-based SNAP experiment with 2,000 SNe betweenz = 0.3 − 1.7 (filled contours). Both experiments are assumed to also use 300 SNebetween z = 0.02 − 0.08. A flat cosmology is assumed (based on Cosmic MicrowaveBackground (CMB) constraints) and the inner (solid line) contours for each experimentinclude tight constraints (from large scale structure surveys) on ΩM , at the ±0.03 level.
For the SNAP experiment, systematic uncertainty is taken as dm = 0.02(z/1.7), andfor the ground-based experiment, dm = 0.03(z/0.5). Such ground-based studies willtest the hypothesis that the dark energy is in the form of a cosmological constant,for which w = −1 at all times. Middle panel: The same confidence regions for thesame experiments not assuming the equation of state parameter, w, to be constant,but instead marginalizing over w", where w(z) = w0 + w"z. (Weller and Albrecht [103]recommend this parameterization of w(z) over the others that have been proposed tocharacterize well the current range of dark energy models.) Note that these plannedground-based studies will yield impressive constraints on the value of w today, w0, evenwithout assuming constant w. In fact, these constraints are comparable to the currentmeasurements of w assuming it is constant (shown in the right panel of Fig. 6). Rightpanel: Estimated 68% confidence regions of the first derivative of the equation of state,w", versus its value today, w0, for the same experiments.
How far can we push the SN measurements? Finding more and more SNe allowsus to beat down statistical errors to arbitrarily small levels but, ultimately,systematic effects will limit the precision to which SNIa magnitudes can beapplied to measure distances. Our best estimate is that it will be possible tocontrol systematic effects from ground-based experiments to a level of ∼ 0.03mag. Carefully controlled ground-based experiments on 200 SNe will reach thisstatistical uncertainty in z = 0.1 redshift bins in the range z = 0.3 − 0.7, and Measuring cosmology with Supernovae is achievable within five years. A comparable quality low redshift sample, with300 SNe in z = 0.02 − 0.08, will also be achievable in that time frame [2].
The SuperNova/Acceleration Probe (SNAP) collaboration1 has proposed to launch a dedicated cosmology satellite [1,68] – the ultimate SNIa experiment.
This satellite will, if funded, scan many square degrees of sky, discovering wellover a thousand SNIa per year and obtain their spectra and light curves out toz = 1.7. Besides the large numbers of objects and their extended redshift range,space-based observations will also provide the opportunity to control many sys-tematic effects better than from the ground [21,53]. Fig. 7 shows the expectedprecision in the SNAP and ground-based experiments for measuring w, assuminga flat Universe. Perhaps the most important advance will be the first studies ofthe time variation of the equation of state w (see the right panel of Fig. 7 and[40,103]).
With rapidly improving CMB data from interferometers, the satellites Mi- crowave Anisotropy Probe (MAP) and Planck, and balloon-based instrumenta-tion planned for the next several years, CMB measurements promise dramaticimprovements in precision on many of the cosmological parameters. However, theCMB measurements are relatively insensitive to the dark energy and the epochof cosmic acceleration. SNIa are currently the only way to directly study thisacceleration epoch with sufficient precision (and control on systematic uncer-tainties) that we can investigate the properties of the dark energy, and any timedependence in these properties. This ambitious goal will require complementaryand supporting measurements of, for example, ΩM from CMB, weak lensing,and large scale structure. The SN measurements will also provide a test of thecosmological results independent from these other techniques, which have theirown systematic errors. Moving forward simultaneously on these experimentalfronts offers the plausible and exciting possibility of achieving a comprehensivemeasurement of the fundamental properties of our Universe.
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