SENTENCIA CONSOLIDADORA DE LÍNEA C-095 DE

After correcting SNe Ia for light curve shape and color, the scatter that remains in the Hubble diagram around the best-fit cosmology is known as the Hubble residual (HR). That is, for each SN Ia the HR is the difference between the value of the distance modulus

obtained from the SN (µSN) and the value obtained from the best-fit cosmology at the

redshift of the SN (µz). If HR scatter is truly random, then the fact that the age, metallicity,

mass, etc. of galaxies evolves with redshift ought not to bias cosmological measurements using SNe Ia. However, if HR is found to correlate with one of these properties, this would pose a problem for cosmology. As it so happens, such correlations have been discovered in recent years.

Gallagher et al. (2005) observed a only a “tenuous” correlation between HR and host metallicity. However, in their subsequent analysis using 17 early-type hosts (Gallagher et al. 2008), such a correlation was seen at 98% confidence for a one-sided test. The trend was such that metal-poor systems tend to produce underluminous SNe Ia after correc-

tion5. The study also found a negligible significance of a correlation between HR and

age. Hicken et al. (2009b) found that after correcting for color and light-curve shape,

SNe Ia in spiral hosts are fainter than those in ellipticals by 2σ, again suggesting different

populations.

The origin of these correlations with HR is not known with certainty, but there is some evidence that it might be due at least in part to variations in the metallicity of the progenitor star. Timmes et al. (2003) showed that SN Ia progenitors (i.e., main sequence

5_{Due an error in the original analysis, this trend is the opposite to what was actually published (Kelly et}

al. 2010; Sullivan et al. 2010).

stars that become white dwarfs) with a higher metallicity Z will have a higher nucleon

density and will generate greater quantities of 14N in the CNO cycle. As He begins

burning in the core, this14N is converted to neutron-rich22Ne, which in turn favors the

synthesis of stable, neutron-rich iron-peak elements54Fe and58Ni at the expense of56Ni.

Since it is the decay of56Ni that powers the light curve, this ultimately results in a fainter

SN Ia. In fact, Timmes et al. (2003) found that a factor of 3 variation in the C, N, O, and Fe

abundances causes a_∼25% variation in the mass of56Ni ejected, with most of the effect

occurring at Z >Z, where Z denotes the solar metallicity. Furthermore, using this

information, Kasen et al. (2009) presented evidence that both peak luminosity and light

curve width decline with Z (see Figure 1.5). However, applying the width-luminosity

relation only partially corrects for this effect since variations in Z cause residual error

due to the different slope and normalization of the width-luminosity relation. Therefore, after correcting for light-curve width, SNe Ia in more metal-rich environments will appear brighter than expected. This prediction is consistent with the HR-metallicity correlation seen by Gallagher et al. (2008).

Howell et al. (2009) used 55 high-redshift SNe Ia from the Supernova Legacy Survey (SNLS) and attempted to reproduce the HR-metallicity correlation seen by Gallagher et

al. (2008) but ruled out such a relation at>99.9%. However, rather than using spectra,

Howell et al. (2009) used photometrically-derived estimates of the host galaxy stellar mass to infer host metallicity via the Tremonti et al. (2004) mass-metallicity relation which states that galaxy metallicity increases with stellar mass. The origin of this relation is believed to be related to the fact that galactic winds are very effective at removing metals from galaxies, but that more massive galaxies have deeper gravitational potential wells from which these metals must escape. Therefore, massive galaxies are better able to counteract these winds and retain their metals (Tremonti et al. 2004). Inspired by Timmes et al. (2003), Howell et al. (2009) also used Arnett’s Rule (Arnett 1979, 1982) to estimate

the mass of56Ni from the peak bolometric luminosity and the rise time of the SN Ia. They

found that host galaxies with a higher inferred metallicity produce SNe Ia with less56Ni

indications that type Ia supernovae are nearly standard (as opposed to

merely standardizable) candles in the near-infrared

27

_.

Without introducing any artificial tuning, the luminosity of the

models correlates with the light-curve decline rate, giving a width–

luminosity relation (WLR) similar to that observed (Fig. 3). A cor-

relation is also found between brightness and the colour measured at

peak. The r.m.s. scatter in the model WLR alone is 24%, while using

both decline rate and colour reduces the dispersion to 21%—similar

to, but slightly greater than, the,16% that is observed

28

_{. The larger}

diversity seen in the models suggests that additional important

physics may constrain the ignition and detonation conditions to a

range narrower than that considered here. As in observations, the

calibration of the models can be improved by using additional

information from the light curve. For example, including the shape

of the light curve in several optical and near-infrared wavelength

bands reduces the scatter to only 15%.

For a given mass of

56

Ni, the residual scatter in the model WLR

reflects individual features of the supernova debris structure. The

turbulent deflagration phase imprints density and chemical inhomo-

geneities, which lead to variations in the timescale for photons to

diffuse out of the debris. In addition, the global asymmetry—due to

asymmetric ignition conditions or off-centre detonation points—

gives rise to anisotropic emission, so that the brightness and duration

of most models vary by 20–30%, depending of the angle from which

they are viewed. Although the adoption of a two-dimensional geo-

metry may exaggerate global asymmetries, spectropolarization

observations reveal that type Ia supernovae typically possess aspheri-

city near or just below the level predicted here

14

_{. Dimmer supernovae}

tend to be more polarized, an observation consistent with our finding

that dimmer models are more asymmetric owing to relatively more

burning in the turbulent deflagration phase.

There are both theoretical suggestions

29

_{and observational indica-}

tions

30

_{that the metallicity of the white dwarf will affect the}

56

_{Ni yield at}

the,10% level. This is because the extra neutrons in trace elements

such as

22

Ne lead to an increased synthesis of neutronized iron group

elements (

54

Fe and

58

Ni) at the expense of

56

Ni. To test the first-order

effect of metallicity on the light curves, we varied the

56

Ni and metal

abundances in the ejecta models according to predicted nucleosyn-

thetic results. The resulting light curves (Fig. 4) show that both the

peak luminosity and light-curve duration decline with metallicity, in

a manner roughly consistent with the WLR. Application of the WLR

should therefore partially correct for metallicity variations, but with a

residual error due to the different slope and normalization of the WLR

at different metallicity. For extreme metallicity variations (from 0.3 to

3.0 times the solar value), this effect can lead to errors in the inferred

distance to the supernova as large as 4%. The actual metallicity

evolution over the range probed by cosmology experiments is much

smaller than this, and we estimate that systematic errors in distance

will probably be less than 2%.

The models suggest that a substantial amount of the scatter in the

observed WLR arises from the random substructures and viewing-

angle effects that are predicted by simulations of multi-dimensional

explosions. In cosmological standard candle applications, these

Peak B-band magntitude

–18.0 –18.5 –19.0 –19.5 –18.0 0.8 1.0 1.2 1.4 1.6 –0.05 0.00 0.05 0.10 0.15 –18.5 –19.0 –19.5 a b B–V colour at maximum B-band decline rate, ΔM₁₅

Figure 3

|

Correlation of the peak brightness of the models with their light- curve duration and colour. The sample includes 44 models each plotted for 30 different viewing angles with equal probability of being observed. Solid circles denote models computed with the most likely range of detonation criteria, while open circles denote more extreme values.a, Relation between the peak brightnessMB(measured in the logarithmic magnitude scale) and the light-curve decline rate parameterDM15, defined as the decrease in B-band brightness from peak to 15 days after peak. The shaded band shows the approximate slope and spread of the observed width–luminosity relation (WLR).b, Relation betweenMBand the colour parameterB2Vmeasured at peak. The solid line shows the slope of the observed relation of ref. 6 but with the normalization shifted, as the models are systematically redder than

observed type Ia supernovae by,7%, probably due to the approximate treatment of non-local thermodynamic equilibrium effects. In observational studies, these two relations are usually fitted jointly as:

MB5MB,01a(s21)2b[(B2V)Bmax1(B2V)0], wheresis a stretch parameter, (B2V)Bmaxis the colour measured at the light curve peak, and MB,0is the fitted B-band magnitude of as51 supernova. We take the colour of a fiducial supernova, (B2V)050, and determine stretch using the first- order relations512(DM1521.1)/1.7. We find for the models fitted values ofa52.25,b54.45 andMB,05 219.27, which are in reasonable agreement with those derived from the recent observational sample of ref. 3:a51.52,

b51.57 andMB,05 219.3115log10(Ho/70), whereHois the Hubble parameter.

0.8 1.0 1.2 1.4 1.6

B-band decline rate, ΔM₁₅

–18.5 –19.0 –19.5

Peak B-band magntitude

Figure 4

|

Effect of the metal content of the progenitor star population on the WLR. The models explore two extreme values of the metallicity: 3 times (red points) and 0.3 times the solar value (blue points). For clarity, each model has been averaged over all viewing angles, and black lines connect similar explosion models of differing metallicity. The coloured lines are linear fits to the WLR of the two metallicity samples separately. The diversity introduced by metallicity variations follows the general width–luminosity trend, but the slightly different normalization and slope of the relation for different metallicity samples indicates a potential source of systematic error in distance determinations.

NATURE

|

Vol 460

|

13 August 2009

LETTERS

871

Macmillan Publishers Limited. All rights reserved

©2009

Figure 1.5 Effect of progenitor metallicity on the width-luminosity relation, reproduced from Kasen et al. (2009). The red points are SN Ia progenitor models with a metallicity

of 3 times the solar value (3Z), while the blue points are models with 0.3 times the solar

metallicity (0.3Z). The metallicity variations are in the general direction of the width-

luminosity relation; however, their effect is not completely corrected for by the relation.

on average, which can be qualitatively explained by the Timmes et al. (2003) result. Using a sample of 168 nearby SNe Ia, Neill et al. (2009) followed up on the work of Howell et al.

(2009) and obtained matched-aperture host galaxy photometry from theGalaxy Evolution

Explorer(GALEX), SDSS, and the Third Reference Catalogue of Bright Galaxies (RC3).

They found that the relation between inferred metallicity and56Ni mass for local hosts

agrees with the Howell et al. (2009) trend at higher redshifts, but is also consistent with no trend. In addition, after imposing cuts to obtain a low-stretch, low-extinction sample

of hosts, they found a 2.1σ correlation between HR and luminosity-weighted age such

that SNe Ia in older hosts appear brighter after correcting for stretch and color. However, this sample contained only 22 hosts and when the full sample was used, they found no such correlation.

Kelly et al. (2010) used_∼60 nearby SNe Ia in the redshift range 0.015<z<0.08 and computed stellar masses of the host galaxies from SDSS photometry. They analyzed their SN sample using two versions of MLCS and two versions of SALT and found the same

result: SNe Ia occuring in massive hosts are_∼10% brighter after light curve correction.

In fact, fitting for a linear relationship between HR (defined as µSN−µz) and host mass

yielded a_∼3σ significance of a non-zero slope. This is shown for the case of SALT2

HRs in Figure 1.6. If the higher-mass galaxies in this sample also have higher metal- licities (following the mass-metallicity relation), this trend agrees with the Gallagher et al. (2008) trend of HR with metallicity and also the theoretical work of Timmes et al. (2003) and Kasen et al. (2009). Kelly et al. (2010) points out the troubling fact that cor- relations between HR and progenitor properties can potentially bias SN Ia cosmological measurements, since progenitors of SNe at high redshift are likely to be younger and more metal-poor than their counterparts at low redshift. The relatively high statistical signifi- cance of this discovery by Kelly et al. (2010) and its implications for cosmology spurred other SN teams to further investigate correlations between HR and host properties in their SN samples.

Sullivan et al. (2010) searched for host-galaxy dependencies using the three-year SNLS sample and the SiFTO light-curve fitter (Conley et al. 2008), which is similar

to SALT2 and parameterizes the light curve by stretch (s) and color (_C). Using stellar

population synthesis models and optical photometry they derived host galaxy properties such as stellar mass and recent star formation per unit mass (known as specific star for-

mation, sSFR). For the SNLS data atz_≤0.85 they found that SNe Ia in low-sSFR host

galaxies, and SNe Ia in massive host galaxies, are systematically brighter by 0.06₋0.09

mag (with significances>3σ) after correcting for SN stretch and color. Assuming host

mass is a proxy for host metallicity and thus metallicity of the progenitor, these results indicate that metal-rich environments host brighter SNe after light-curve correction. This agrees with the previously published trends described above, and their results are also consistent with the progenitor metallicity-luminosity relation of Timmes et al. (2003) and

752

KELLY ET AL.

Vol. 715

(a) _(b)

Figure 5.Trends in MLCS17 and SALT2 Hubble residual with host stellar mass (logM >9.5). SNe with more massive hosts have Hubble residuals that are more

negative in the cases of (a) MLCS17 and (b) SALT2, consistent with the trend evident in Figure4. Host stellar masses were measured using fits tougrizphotometry

with the PEGASE2 stellar population synthesis templates. The weighted averages of two bins separated by their masses yield a magnitude difference of 0.11 (2.3σ;

58) for MLCS17 and 0.11 (2.5σ; 60) for SALT2. When we fit for the trend with host stellar mass (α) while holdingβ₌γ ₌0, only 0.2% (2.8σ; 58) of slopes drawn

from an MCMC analysis are greater than zero for MLCS17 and 0.4% (3.0σ; 60) for SALT2. In parentheses is the significance of a non-zero slope followed by the

number of SNe included in the fit. The upper panels plot the posterior slope distributions. (A color version of this figure is available in the online journal.)

Table 9

Improvement in the Standard Deviation of Hubble Residuals after Subtracting Host-dependent Trend

Sample MLCS17 MLCS31 SALT SALT2

90% radius 0.193_\0.184 0.222_\0.210 0.168_\0.156 0.185_\0.175

90% radius (<30 kpc) 0.191_\0.185 0.219_\0.212 0.161_\0.157 0.182_\0.177

logM 0.193_\0.182 0.222_\0.208 0.168_\0.167 0.185_\0.178

logM(>9.5;GALEX, Neill 09) 0.159_\0.143 0.192_\0.180 0.174_\0.159 0.163_\0.150

logM(GALEX, Neill 09) 0.181_\0.151 0.213_\0.187 0.174_\0.158 0.184_\0.158

Notes. The first value is the standard deviation in magnitudes before, and the second value is the standard deviation in magnitudes after

subtracting the trend with host property,α_×(host property), determined from fits where we holdβ₌γ ₌0.

Table 10

Improvement in the Standard Deviation of Hubble Residuals after Subtracting Host-dependent Trend from Simultaneous Fit

Sample MLCS17 MLCS31 SALT SALT2

90% radius 0.193_\0.184 0.222_\0.210 0.168_\0.156 0.185_\0.175

90% radius (<30 kpc) 0.191_\0.185 0.219_\0.212 0.161_\0.157 0.182_\0.177

logM 0.193_\0.183 0.222_\0.211 0.168_\0.168 0.185_\0.180

logM(>9.5;GALEX, Neill 09) 0.159_\0.142 0.192_\0.180 0.174_\0.158 0.163_\0.150

logM(GALEX, Neill 09) 0.181_\0.151 0.213_\0.188 0.174_\0.158 0.184_\0.158

Notes.First value is the standard deviation in magnitudes before, and the second value is the standard deviation in magnitudes after subtracting the trend with host property,α_×(host property), but not the trends with light curve properties (β,γ). Here the trend with host property (α) is

determined in fits where we simultaneously fit for trends with light curve parameters (β,γ). 6.5.1. Neill et al. (2009) Masses

We now repeat the analyses using stellar mass estimates

from Neill et al. (2009), which were fitted using

GALEX

UV measurements in addition to SDSS

u

"

g

"

r

"

i

"

z

"

magnitudes.

Because each Neill et al. (2009) host galaxy is required to

have UV as well as optical measurements, Neill et al. (2009)

measured masses for only 49 of the 70 SNe in our sample

with MLCS17

AV

<

0.5. Fitting only for a trend in Hubble

residuals with host galaxy mass (α) while holding

β

₌

γ

₌

0, the significance of a non-zero slope (α) ranges from 2.3σ

to 2.7σ

depending on the light curve fitter. The significance of

a difference between the bins’ weighted averages ranges from

1.8σ

to 3.2σ

among the light curve fitters.

Simultaneously fitting for and marginalizing over linear

trends (β,γ) with light curve parameters, the significance of

a non-zero slope (α) is 1.9σ

for all light curve fitters. The

joint posterior probability distributions do not reveal strong

degeneracies between the fit coefficients. Removing the best-

fitting trends with light curve parameters (β,γ) from the Hubble

residuals after the simultaneous fit, a 1.6σ–2.5σ

(2.1σ–2.5σ

without SALT2) difference between the bin weighted averages

remains.

Figure 1.6 Correlation between Hubble residual (HR=µSN−µz) and host galaxy stellar

mass, reproduced from Kelly et al. (2010). The weighted averages of the two mass bins

(shown as the black crosses) differ by 0.11 mag (2.5σ). A linear fit to the data (bold

black line) reveals a 3.0σ significance of a non-zero slope. The upper panel shows the

posterior probability distribution of the slope obtained from the Markov Chain Monte Carlo (MCMC) fitting procedure.

Kasen et al. (2009). The plot from Sullivan et al. (2010) of the HR correlation with host mass is shown in the top panel of Figure 1.7. Mean residuals in bins of mass are shown

in red. SNe in the 3 lowest mass bins are fainter than those in the 2 highest bins at 3.9σ

significance. In addition, Sullivan et al. (2010) proposed a bimodal correction using two absolute magnitudes for SNe Ia: one for those in low-mass hosts and a different one for those in high-mass hosts. They claim such a correction removes host dependence and

improves cosmological fits by_∼4σ.

Similar results were also discovered in the SDSS-II SN Survey data. Lampeitl et al. (2010) used the full three-year sample but restricted the analysis to the 361 SNe Ia

No. 1, 2010 HOST GALAXY DEPENDENCES OF SNe Ia 573

Figure 5.Same as Figure4, but for SNe in star-forming host galaxies. The dashed lines are for the restricted subset of SNe discussed in Section3.1. (A color version of this figure is available in the online journal.)

Figure 6.Residuals around the best-fit Hubble diagram as a function of host galaxy stellar mass (calculated from P ´EGASE2). The (red) solid circles are for passive host galaxies, while the (blue) open squares are star-forming hosts. The inclined triple-dot-dashed line is the best-fit to these data, while the dot-dashed line is the fiducial three-parameter SALT2 fitted model (Equation (1)) without regard to the host galaxy stellar mass or type.

(A color version of this figure is available in the online journal.)

Criteria (BIC; Liddle 2004). BIC is a penalized likelihood statistic that accounts for models with different numbers of parameters, and we find that the BIC score for Equation (2) is 117 compared to 134 for Equation (1). The smaller BIC score demonstrates that the additional parameter is justified.

5. CONCLUSIONS

We present an analysis of the host galaxy dependences for the SDSS-II Supernova Survey. We have used 361 SNe Ia (see Table1) taken from the full three years of this survey and then applied several data cuts to ensure that we have a clean, well- understood, sample of low-redshift SNe (z < 0.21). We have

analyzed these data using two well-known light-curve fitting

In document Línea Jurisprudencial de la Corte Constitucional sobre el Principio de Gratuidad en la Administración de Justicia y sus Excepciones en Colombia (página 103-112)