Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.eso.org/~bleibund/papers/Cargese2.ps Дата изменения: Mon Aug 15 21:18:02 2005 Дата индексирования: Tue Oct 2 02:55:58 2012 Кодировка: Поисковые слова: dark energy

Chapter 1
COSMOLOGY WITH SUPERNOVAE
Bruno Leibundgut 1
1 European Southern Observatory
Karl-Schwarzschild-Strasse 2, D-85748 Garching
Germany
bleibundgut@eso.org
Abstract Modern cosmology is using many dierent methods to determine the
structure of the universe. Supernovae are among the most important
ones due to their extreme luminosity, the time-variability that allows to
separate the dierent supernova explosions and relative ease with which
they can be observed.
Since the recognition of supernovae as a separate class of astrophys-
ical objects they have been proposed and used to measure the distance
scale and the geometry of the universe.
There are several independent applications with supernovae to mea-
sure the current expansion rate, Hubble's constant, and the expansion
history of the universe. The latter has led to the surprising discovery
that the expansion is actually accelerating and a new component for the
universe is needed. Supernovae are also poised to be a major player in
the characterisation of the nature of the dark energy.
Keywords: Cosmology - supernovae - distance scale
1. Introduction
Cosmology with supernovae has developed over the second half of the
last century. Their extreme luminosities always made them attractive
candidates to measure large distances. Various methods were devised to
use supernovae to measure cosmological parameters ranging from simple
standard candle paradigms to physical explanations of the supernova ex-
plosions and subsequent derivation of distances. Essentially, supernovae
have been used to determine luminosity distances, i.e. the comparison

2
of the observed ux to the total emitted radiation. The trick is to nd
a reliable way to measure the absolute luminosity of the objects.
There are two major cosmological parameters that can be determined
through supernova observations. They are the classical parameters,
which govern the expansion of the universe in Friedmann-Robertson-
Walker models: the Hubble constant, H 0 , and the deceleration parame-
ter, q 0 . The former sets the scale of the universe and the magnitude of
the current expansion of space and the latter describes the change of the
expansion with time (e.g. [53, 54, 63, 41, 40]). There is a rich literature
on the Hubble constant and Type Ia supernovae (SNe Ia) (see [4, 5, 31]
for reviews). The deceleration parameter has been replaced by more
modern formulations specically including the cosmological constant or
some variants thereof [7].
2. The Hubble constant
Type Ia supernovae
The best way to show that objects provide good luminosity distances
is to plot them in a Hubble diagram. Originally, this diagram was us-
ing recession velocity vs. apparent magnitude [24, 53]. The underlying
assumptions are that the Hubble law holds and that the objects are
all of the same luminosity, i.e. standard candles, so that the apparent
brightness directly re ects distance.
Since no astronomical standard candle is known { all proposed objects
have been shown to be essentially non-uniform in one way or another
{ we nowadays have to calculate and plot the distance modulus for the
objects. The scatter around the linear expansion line is less than 0.2
magnitudes or 20% [61]. Independent of our ignorance of the exact
explosion mechanism or the radiation transport in the explosions this
proves that SNe Ia can reliably be used as a distance indicator in the
local universe. This situation is very much comparable to the Cepheid
stars, where the period-luminosity relation is based on empirical data of
objects in the Magellanic Clouds.
The simplest method is to assume that all supernovae are identical.
This is, of course, not true (see previous paper) but it turns out that the
subclass of the Type Ia supernovae is indeed rather homogeneous. The
rst to plot a Hubble diagram of Type Ia Supernovae was Kowal [26].
There are essentially three quantities that can be derived from such a
Hubble diagram in the nearby universe: the slope of the expansion line,
the scatter around the expansion line and the value of the local Hubble
constant from the intercept at zero redshift (e.g. [60, 33]). The slope
gives an indication of the local expansion and for a linear expansion in an

Cosmology with Supernovae 3
Figure 1.1. Hubble diagram of nearby Type Ia supernovae. The distances are derived
from light curve shape corrected luminosities (data from [61]). The solid line is for
an empty
universe(

=
M = 0), the dotted line for an Einstein-de Sitter model
(
 =
0;
M = 1) and the dashed line for a model with no matter and all cosmological
constant(
 =
1;
M = 0). The concordance
model(
 =
0:7;
M = 0:3) is shown
as the line tting the data best. The bottom panel shows all distances relative to the
empty universe model.
.01 .1 1
35
40
45
(m­M)
.01 .1 1
­1
­.5
0
.5
1
redshift z
D(m­M)
isotropic universe it has a xed value. The scatter around the expansion
line provides a measure of the accuracy of the standard candle and the
measurement errors. The intercept of the line, nally, together with
an estimate of the absolute luminosity gives the Hubble constant. It
has become clear that SNe Ia in the optical are not standard candles
and have their luminosity normalised to be used as distance indicators
[45, 22, 48, 49, 43, 46, 17]. A systematic comparison of these dierent
methods has been done [12, 30] and it has been shown that they are not
internally consistent. The reason for this technical problem is still not
clear and needs to be investigated. More accurate light curve data are
becoming available (e.g. [27, 37, 38, 28, 6, 3]) and it should be possible
to further investigate the correlations between light curve shape, colour
and luminosity of SNe Ia. For these reasons modern Hubble diagrams
show the distance modulus (m-M) rather than the directly observed
apparent magnitude m. The latest version with over 200 SNe Ia has been
assembled by Tonry ([61] see also [2, 51]) and is shown in Figure 1.1.
It should be noted that SNe Ia may be standard candles in the near-

4
infrared [29]. The rst signicant IR sample shows very small scatter
without prior correction for light curves shape. For the derivation of
the Hubble constant the (normalised) luminosity of the SNe Ia has to
be known. The most direct way to achieve this is through the distance
ladder and in particular the calibration of nearby SNe Ia by Cepheids
(for the most recent results see [52, 16]). The main discrepancy for the
published values of the Hubble constant from SNe Ia is coming from
the dierent interpretations of the Cepheids and application of the light
curve shape correction.
Core-collapse supernovae
The brilliance of core-collapse supernovae has enticed people to inves-
tigate their capabilities as distance indicators as well. Following early
work by Baade [1], originally done for Cepheid stars, the expanding pho-
tosphere method (EPM, [13]) has been applied to several supernovae.
The most comprehensive data sample has been assembled by Hamuy
[18]. A critical test has become the distance to SN 1999em, which was
determined through EPM [35, 20, 14] and which also has a Cepheid dis-
tance available [36]. The discrepancy is most likely attributable to the
fact that the correction factor for the dilution of the black body ux in
EPM are strongly model dependent and need to be calculated for each
supernova individually.
Recently, Mario Hamuy has realised that the expansion velocity and
the luminosity during the plateau phase correlate and that Type II
SNe may be quite good distance indicators [21]. The distance accu-
racy achieved this way can be better than 20%. These determinations
are based on the physical understanding of the plateau phase of SNe II
and are linked to physics of the supernova atmosphere. This means that
they are independent of the distance ladder, which is needed, e.g., for
the SNe Ia. Typical values for the Hubble constant from SNe II are in
the range of 65 to 75 km s 1 Mpc 1 [19].
3. The expansion history of the universe
The recent paradigm changes in the cosmological model are based on
several new insights. The atness of space-time as measured by the cos-
mic microwave background (CMB) uctuations and the recognition, that
the global matter density is near 30% of the critical density, require an
additional component in the energy content of the universe. At the same
time the observation that the luminosity distances derived from Type
Ia supernovae are larger than the expectation in any non-accelerated
universe model have conspired to change our view of the history of the

Cosmology with Supernovae 5
cosmic expansion. The three measurements are complementary to each
other and the combination of any two of them provides independent ev-
idence for an additional component in the Friedman equation. However,
only the supernova measurement gives a direct indication that we need
a repulsive component in the universe. It will also be the supernovae
that will provide a rst indication to the nature of the dark energy.
There are several fundamental tests that will need to be performed
until we can be sure that the current paradigm will persist. It is very
appealing to think we know all constituents of the universe by now,
but further surprises may still be in store for us. The testing has to
concentrate on the reliability of the individual measurements. The Type
Ia supernovae have been criticised for the fact that they are based on a
rather simple assumption, namely that the distances derived from them
are accurate. Many publications oversimplify this picture by calling
Type Ia supernovae standard candles. This is not only incorrect, also it
is misleading and belittles the result. The tests done on supernovae are
solid and the theoretical work is progressing steadily.
Since SNe Ia are not standard candles, it is not admissible to simply
assume a constant luminosity. Instead, one has to adopt that the lumi-
nosity normalisation of the distant objects follows what has been found in
the nearby sample. Although the High-z Supernova Search Team (HZT;
[55, 49, 61, 2]) and the Supernova Cosmology Project (SCP; [44, 25])
make this assumption in dierent forms, it is essentially identical. The
SCP derives the corrections from all supernovae in their sample, i.e.
nearby and distant ones, while the HZT derives the correlations from
the (large) nearby sample and applies it to the distant objects (cf. [32]).
It is also interesting to note that the SCP claims that both light curve
shape correction and correction for host galaxy reddening aect their
result rather little [44, 25]. On the other hand, the normalisation and
absorption correction done by the HZT (in three dierent implemen-
tations) are important for the cosmological result. This discrepancy
between the two teams will need to be resolved at some point.
4. Universal acceleration according to Type Ia
supernovae
We will describe here the current status of the supernova research and
outline ongoing projects to distinguish between a cosmological constant
or a vacuum density contribution to the energy-momentum tensor in the
Einstein equation.
Type Ia supernovae measure luminosity distances to objects out to
about a redshift of 1. These distances are the most accurate currently

6
available to astronomers for cosmological purposes, i.e. beyond the
Coma cluster distance. Since the luminosity distances depend on the
evolution of the Hubble parameter and this in turn depends on the en-
ergy content of the universe through the Einstein equation (e.g. [7]) one
can derive the energy sources dominating over the lookback time cov-
ered by the observations (see [47, 31, 42] for a detailed review). Once
the luminosity distances are derived from the supernova data a likeli-
hood calculation provides the most statistically suitable values for the
complete supernova data under certain assumptions, like the neglect of
dust and evolution. It is pointless to divide the supernova data into
subsamples that do not cover the complete redshift range as the eect is
not detectable on smaller scales. Figure 1.1 shows that the current data
by far do not warrant such a treatment (as proposed by [39, 8, 62]).
The largest available data set is provided by Barris et al. [2], which
includes a signicant set of supernovae at redshifts near 1. This data set
conrms the earlier results of the HZT (cf. Fig. 1.2) and is consistent
with the most recent result of the SCP [25]. All astrophysical eects, like
dust or evolution of the supernovae, have been ignored in this deriva-
tion. The HZT applies a correction for dust in the Milky Way and the
host galaxy of the supernova directly. Only if dust at high redshift is
systematically dierent from the one in our galaxy, is this correction bi-
ased. Recent detection of 850m emission from host galaxies at z  0:5
shows that dust is present in some of these galaxies [15], although the
amount may be negligible for the supernova cosmology. These results
are in contrast with the claim by Sullivan et al. [59] that the reddening
of distant supernovae in spiral galaxies is very small, when these objects
are compared to the SN data from dust-free elliptical galaxies. The
reddening derived by Tonry et al. [61] for distant SNe Ia is typically
smaller than the one found for nearby objects. This is not surprising
considering that the distant searches are mostly ux limited and will
not nd many heavily extincted objects, while the nearby supernovae
are drawn from a large heterogeneous sample, which in several cases
includes highly reddened objects. There might be secondary selection
eects at work as well, like the fact that the distant supernovae often
have larger projected distances from their hosts than nearby ones. A last
indication that dust is not a severe problem is the fact that among the
rst distant SNe Ia of the HZT were very blue [31] objects. In fact, six
out of nine objects were bluer than their nearby counterparts. Although
this has now been claimed to possibly be a selection eect [25], it is not
clear whether this indeed is the case, as the eect should be redshift
dependent, which it seems not to be, judging from the small sample in
[31]. The recent publication by the SCP [25] does not nd the same

Cosmology with Supernovae 7
eect for the objects which have multi-wavelength light curves. Further
analysis of the K-corrections and the dust properties is clearly required.
Evolution is another potential eect, which could mimic a cosmolog-
ical signal. This is much harder to control. For reasonable predictions
of how progenitor metalicity or age could aect the brightness of SNe Ia
one needs a detailed model of the explosion and the radiation escape
from the explosion [23]. Both are unsolved problems. A detailed study
of the properties of the SN host galaxies has not shown any correlation
with supernovae distances or properties [64]. Progress can only be made
through detailed observations of bright, nearby SNe Ia at all phases.
Recent data sets are very encouraging [27, 28, 3] (for a review see [32]).
In addition to the detailed spectral, light and colour curve data one can
use bolometric light curves to derive the total emitted radiation from
the explosion [10, 11]. The latter provides important information on the
physical parameters that govern the explosion, like mass of synthesised
nickel and the ray escape fraction at late times.
With no clear indication of evolution, the simplest assumption is to
disregard any evolutionary eects; a very dangerous approach, if it goes
unchecked. This is the reason that the HZT has spectroscopically con-
rmed its distant SNe Ia. The spectra have been published together
against the light curve data [49, 61, 2] and separately for a few objects
[9, 34]. While the signal for some of the distant supernovae is not very
good, and in a few early cases the SN classication may even be doubt-
ful, there are no obvious strong deviations from the spectral appearance
of the nearby supernovae. In some cases, the supernova spectra can be
used to determine the phase of the distant SNe Ia and to check it with
the light curves directly. This provides an independent consistency argu-
ment that the distant supernovae behave rather similar to their nearby
counterparts. This means that the distant supernovae cannot be very
dierent from the nearby ones. Yet, the colour of the distant objects ap-
pears to be systematically bluer. This could be the signature of evolution
and will need to be worked out in more detail.
Luminosity distances over a limited redshift range result in degenerate
likelihood distributions in
the

vs:
M plane along a line corresponding
roughly
to

1:4
M = 0:35  0:14 [44, 61] (cf. Fig. 1.2). These leads
to an increased uncertainty along this direction. It should be noted that
the most recent determinations of the cosmological parameters by the
HZT favour values that are rather dierent from a at universe solution
[61, 2]. If the universe indeed has a at geometry, as suggested by the
CMB data (e.g. [57]) then this would be an indication of some unresolved
systematic eect. The SCP has not observed a similar trend [25], but the

8
Figure 1.2. Likelihood distribution
for

vs:
M . The input data are from [61].
This diagram should be compared to similar ones in [49, 44, 47, 31, 42, 2, 25]. The
degeneracy along
0:8

0:6
M is obvious. The overlap with the at universe model
is not within the 68% likelihood area here. The grey contour lines show the dynamical
age of the universe H0
t0 . Clearly the SN data favour an age near 1.
redshift range of their published data does not extend beyond z  0:8
so far.
5. Characterising dark energy
It has been generally accepted that a large fraction of the energy
content of the universe is in a form very similar to the vacuum energy
or a cosmological constant. Competing theories have been developed
to explain the low, but non-zero, value of this energy form. An often

Cosmology with Supernovae 9
used description is the equation of state parameter (w = p
c 2 ), which
in the case of dark energy has to be negative, i.e. contain negative
pressure p, as the energy density  has to be positive (c stands for the
speed of light). With w < 1
3
the universe is actually accelerating.
For eld theories w is most likely variable with time and dierent from
the value for a cosmological constant (w = 1). The transition from a
matter dominated
universe(
M
>
 ) happened sometime during the
second half the history of the universe, 0:4 < z < 0:8. It should hence
be possible to determine this transition and then map the change as a
function of redshift in the interval 0:2 < z < 0:8. With a well-calibrated
and controlled data set of SNe Ia in this redshift interval it should be
possible to accurately map the transition and determine the strength of
the dark energy and the (integrated) value of w. Several projects have
embarked on such a project. The HZT has started the ESSENCE project
with the search and photometry carried out with the CTIO Blanco 4m-
telescope with the supporting spectroscopy from VLT, Gemini, Keck,
Magellan and MMT. The goal is to have 200 spectroscopically conrmed
SNe Ia with densely sampled light curves in at least two lters evenly
distributed in redshift with z < 0:8 [56]. The CFHT Legacy Survey
is aiming for about 900 SNe Ia out to a slightly larger redshift with
spectroscopy from VLT, Keck, Gemini and Magellan. In the future the
SNAP satellite, in the meantime renamed to Joint Dark Energy Mission
(JDEM), should observe about 2000 SNe Ia out to z < 1:7.
The supernovae cannot do this alone. They will require an accurate
determination of the matter
density
M from a dierent source. The
required accuracy of this parameter should be a few percent (cf. [61]).
In the meantime a survey for supernovae has been done within the
GOODS collaboration. The goal was to nd and follow supernovae at
redshift larger than 1.2, which was achieved for about one third of the
sample [50]. Spectroscopic conrmation of 18 supernovae (nine with
z > 1) is available [58, 51]. Some of the distant objects could not be
classied with a spectrum and rely on a spectroscopic redshift from the
host galaxies only. These data
constrain
M more accurately than was
possible so far, as the supernovae are in the deceleration portion of the
Hubble diagram. They also show that evolutionary eects are not likely
to explain the faintness of SNe Ia near z=0.5 and the change to more
luminous objects at redshifts beyond z=1.
6. Conclusions
Supernovae at cosmological distances have provided some of the most
accurate determinations of the Hubble constant. It is by now clear that

10
the largest (systematic) uncertainties stem from the calibration of the
local distance indicators, like the Cepheids. An intriguing result con-
cerning the expansion history of the universe and its energy contents
has emerged from the observations of very distant SNe Ia. The evidence
for a cosmological constant or an energy eld acting very similarly is
strong and generally accepted. The future supernova observations have
to concentrate on two aspects. One is to determine the (integrated)
equation of state parameter for the dark energy to possibly distinguish
between a pure cosmological constant and a scalar particle eld. Sec-
ondly to control any evolution of the supernovae, which potentially could
aect the cosmological result, it is mandatory to constrain the models
with exquisite data from nearby supernovae. These projects are under
way and we can expect to make signicant progress in both directions
very soon.
References
[1] Baade, W. 1926, AN, 228, 359
[2] Barris, B., et al., 2004, ApJ, 602, 571
[3] Benetti, S., et al., 2004, MNRAS, 348, 261
[4] Branch, D., Tammann, G.A., 1992, ARA&A, 30, 359
[5] Branch, D., 1998, ARA&A, 36, 17
[6] Candia, P., et al. 2003, PASP, 115, 277
[7] Carroll, S.M., Press, W.H., Turner, E.L 1992, ARA&A 30, 499
[8] Choudhury, T. R., Padmanabhan, T., 2004, MNRAS, in press (astro-
ph/0311622)
[9] Coil, A.L., et al., 2000, ApJ, 544, L111
[10] Contardo, G., Leibundgut, B., Vacca, W. D., 2000, A&A, 359, 876
[11] Contardo, G., PhD Thesis, Technical University Munich
[12] Drell, P.S., Loredo, T.J., Wasserman, I., 2000, ApJ, 530, 593
[13] Eastman, R. G., Schmidt, B. P., Kirshner, R. P. 1996, ApJ. 466,
911
[14] Elmhamdi, A., et al. 2003, MNRAS, 338, 939
[15] Farrah, D, Meikle, W. P. S., Clemens, D., Rowan-Robinson, M.,
Mattila, S., 2002, MNRAS, 336, L17
[16] Freedman, W.L., et al., 2001, ApJ, 553, 47
[17] Goldhaber, G., et al., 2001, ApJ, 558, 359
[18] Hamuy, M. 2001, PhD Thesis, Tucson: University of Arizona

Cosmology with Supernovae 11
[19] Hamuy, M. 2003, ApJ, 582, 905
[20] Hamuy, M., et al. 2002, AJ, 124, 417
[21] Hamuy, M., Pinto, P. A. 2002, ApJ, 566, L63
[22] Hamuy, M., et al. 1996, AJ, 112, 2438
[23] Hillebrandt, W., Niemeyer, J. C., ARA&A, 38, 191
[24] Hubble, E., The Realm of the Nebulae, 1936, (New Haven: Yale
University Press)
[25] Knop, R., et al., 2004, ApJ, 598, 102
[26] Kowal, C. T. 1968, AJ, 73, 1021
[27] Krisciunas, K., et al., 2001, AJ, 122, 1616
[28] Krisciunas, K., et al., 2003, AJ, 125, 166
[29] Krisciunas, K., Phillips, M.M., Suntze, N.B., 2004, ApJ, 602, L81
[30] Leibundgut, B., 2000, A&AR, 10, 179
[31] Leibundgut, B., 2001, ARA&A, 39, 67
[32] Leibundgut, B., Suntze, N. B., in Supernovae and Gamma{Ray
Bursts, ed. K. Weiler, (Heidelberg: Springer), 77
[33] Leibundgut, B., Pinto, P.A., 1992, ApJ, 401, 49
[34] Leibundgut, B., Sollerman, J., 2001, Europhysics News, 32, 4
[35] Leonard, D. C., et al. 2001, PASP, 114, 35
[36] Leonard, D. C., et al. 2003, ApJ, 594, 247
[37] Li, W., et al., 2001, PASP, 113, 1178
[38] Li, W., et al., 2003, PASP, 115, 453
[39] Padmanabhan, T., Choudhury, T. R., 2003, MNRAS, 344, 823
[40] Peacock, J.A., 1999, Cosmological Physics, Cambridge: Cambridge
University Press
[41] Peebles, P.J.E., 1993, Principles of Physical Cosmology, Princeton:
Princeton University Press
[42] Perlmutter, S., Schmidt, B. P., in Supernovae and Gamma-Ray
Bursts, ed. K. Weiler, (Heidelberg: Springer), 195
[43] Perlmutter, S., et al., 1997, ApJ, 483, 565
[44] Perlmutter, S., et al., 1999, ApJ, 517, 565
[45] Phillips, M. M., 1993, ApJ, 413, L105
[46] Phillips, M.M., Lira, P., Suntze, N.B., Schommer, R.A., Hamuy,
M., Maza, J., 1999, AJ, 118, 1766
[47] Riess, A. G., 2000, PASP, 112, 1284
[48] Riess, A. G., Press, W. M., & Kirshner, R. P., 1996, ApJ, 473, 88

12
[49] Riess, A. G., et al., 1998, AJ, 116, 1009
[50] Riess, A. G., et al., 2004, ApJ, 600, L163
[51] Riess, A. G., et al., 2004, ApJ, in press (astro-ph/0402512)
[52] Saha, A, Sandage, A., Tammann, G.A., Labhardt, L., Macchetto,
F.D., Panagia, N., 1999, ApJ, 522, 802
[53] Sandage, A., 1961, ApJ, 133, 355
[54] Sandage, A., 1988, ARA&A, 26, 561
[55] Schmidt, B.P., et al., 1998, ApJ, 507, 46
[56] Smith, R. C., et al. 2002, BAAS, 78.08
[57] Spergel, D. N., et al., 2003, ApJS, 148, 175
[58] Strolger, L., et al., AJ, submitted
[59] Sullivan, M., et al., 2003, MNRAS, 340, 1057
[60] Tammann, A.G, Leibundgut, B., 1990, A&A, 236, 9
[61] Tonry, J. L., et al., 2003, ApJ, 594, 1
[62] Wang, Y., Mukherjee, P., 2004, ApJ, submitted (astro-ph/0312192)
[63] Weinberg, S., 1972. Gravitation and cosmology: principles and ap-
plications of the general theory of relativity, New York: Wiley
[64] Williams, B. F., et al., 2003, AJ, 126, 2608