TYPE Ia SUPERNOVAE RATES AND GALAXY CLUSTERING FROM THE CFHT SUPERNOVA LEGACY SURVEY

The importance of understanding Type Ia supernovae (SNe Ia) has risen greatly in recent years because of their pivotal role in demonstrating the accelerated expansion of the universe (Riess et al. 1998; Perlmutter et al. 1999; Astier et al. 2006; Wood-Vasey et al. 2007). SNe Ia are generally agreed to be carbon–oxygen white dwarfs which have accreted sufficient mass from their companion star to initiate a thermonuclear explosion. Despite this consensus, several models exist for the companion type, the accretion process, the delay time between star formation and SN Ia explosion, and the explosion mechanism (Hillebrandt & Niemeyer 2000; Höflich et al. 2003). Photometric and spectroscopic observations, and explosion simulations, are making inroads towards a coherent picture of SN Ia events (Mazzali et al. 2007). Another (albeit indirect) path of investigation is studying the SN Ia rate in different stellar populations.

Compilation of the Cappellaro et al. (1999) supernova catalog with infrared data led Mannucci et al. (2005) to conclude that SN II, SN Ib/c, and SN Ia rates per unit stellar mass are directly correlated with host morphology and (B − K) color, and to infer a correlation with host star formation activity. Based on this, Scannapieco & Bildsten (2005) expressed the SN Ia rate per unit stellar mass as the sum of a "delayed" component from old and a "prompt" component from young stellar populations. They parameterized the two components as A and B, proportional to the mass and star-formation rate (SFR) of a galaxy respectively, and also found the "prompt" component to account for the discrepancy between low observed rates of cluster SNe Ia and the high cluster iron abundance (Maoz & Gal-Yam 2004). This "A + B" two-component model has since been confirmed at intermediate redshifts with the large SNLS catalog (Sullivan et al. 2006a); the observations can also be matched with progenitor populations that have distributions of delay times as described by Mannucci et al. (2006) and Pritchet et al. (2008).

From the two-component model, the SN Ia rate in galaxy clusters is expected to be lower than in the field due to the morphology–density relation (Postman & Geller 1984): cluster galaxies are predominantly of early type with little or no star formation. However, since clusters contain only a small fraction of the stellar mass of the universe, it is conceivable that some hitherto undetected influence in such exotic environments could affect the SN Ia rate. For example, the fraction of binary stars, or the rate of mass accretion onto the white dwarf, could be enhanced. The recent discovery of an enhanced nova rate in the core of elliptical galaxy M87 is evidence for the latter (Madrid et al. 2007). A second example is the detected SN Ia rate enhancement in radio-loud early-type galaxies (Della Valle et al. 2005); such galaxies tend to be very luminous ellipticals in the centers of large clusters.

Based on their analysis of two SN found in an archival survey of Hubble Space Telescope cluster images, Gal-Yam et al. (2002) find the SN Ia rate in cluster and field galaxies to be consistent at both low and high redshifts. The Wise Observatory Optical Transient Survey (WOOTS; Gal-Yam et al. 2008) targeting 140 Abell clusters confirmed the SNe Ia rate per unit mass in low-redshift galaxy clusters to be consistent with the rate in early-type galaxies (Sharon et al. 2007). Recently, Mannucci et al. (2007) analyzed the Cappellaro et al. (1999) sample of 136 low-redshift SNe (z < 0.04) and found the SN Ia rate in cluster early-type galaxies is enhanced by a factor of ≳3 over field early-type galaxies. The large database of intermediate to high redshift SNe Ia compiled by the Canada–France–Hawaii Telescope Supernova Legacy Survey (CFHT SNLS) (Astier et al. 2006), and the publicly available photometric redshift galaxy and cluster catalogs for SNLS fields (Ilbert et al. 2006; Olsen et al. 2007) are ideal for extending these investigations to higher redshifts. As the SNLS is not a cluster-targeted survey, further advantages over Sharon et al. (2007) include using a flexible parametrization of galaxy clustering in the environments of SNe Ia, and determining simultaneous field SN Ia rates for comparison to cluster rates.

Section 2 describes the SN Ia, galaxy, and cluster catalogs used in this experiment. Sections 3 and 4 present two independent approaches to statistically evaluate the effects of clustering on the SN Ia rate per unit mass. Section 3 uses a continuous clustering strength estimator to compare the SN Ia rate per unit mass inside and outside clustered environments. Section 4 identifies six SNe Ia in Olsen et al. (2007) galaxy clusters, considers the probability of these observations based on expectations from the two-component rate model, and calculates the SN Ia rate per unit mass in clusters. Section 5 reviews and discusses the paper's main findings.

A flat cosmology with H₀ = 70 km s⁻¹ Mpc⁻¹, Ω_Lambda = 0.7, and Ω_M = 0.3 is used.

Three catalogs are described here, all of which were generated from the four Deep fields of the CFHT Legacy Survey: the Supernova Legacy Survey catalog of type Ia supernovae¹¹, the Ilbert et al. (2006) photometric redshift galaxy catalog, and the Olsen et al. (2007) optical galaxy cluster catalog.

2.1. The CFHT Supernova Legacy Survey Catalog

2.2. Ilbert Photometric Redshift Galaxy Catalog

2.3. Olsen Optical Galaxy Cluster Catalog

2.4. Additional Catalog Processing

To begin we use a continuous clustering strength estimator to compare the SN Ia rate per unit mass in and out of clustered environments. This parameter quantifies the significance (Σ) of finding N_E neighbor galaxies, the environment of a galaxy or SN Ia, given number expected from the background distribution. Σ is calculated for a cylindrical volume environment of diameter D and redshift depth ±σ_Δz/(1+z)(1 + z) (σ from Section 2.4) centered on the object, as in Equation (1) where N_E is the number of galaxies in the environment, N_F is the number of galaxies within ±σ_Δz/(1+z)(1 + z) in the Deep field, A_E = πD²/4 is the aperture area, and A_F is the area of the field after allowing for the area occulted by foreground star masks (Ilbert et al. 2006). Since N_F is computed at the same redshift as the object being studied, incompleteness at high redshift is automatically compensated for:

$$\begin{equation} \Sigma = \frac{N_E-N_F(A_E/A_F)}{\sqrt{N_F(A_E/A_F)}}. \end{equation} \tag{ 1 }$$

The advantage of this parametrization is that a strict cluster definition is avoided—any desired scale of clustering can be explored by altering the aperture diameter D. Environmental significances are calculated using a range of clustering scales (diameters D ranging from 0.1 to 1.5 Mpc) both for field galaxies (0.1 < z < 1.1), and also for the 232 SNe Ia surviving the cuts in Section 2.4. Normalized cumulative significance distributions for both field galaxies and SNe Ia are shown in Figure 1 for D = 0.6 Mpc. A Kolmogorov–Smirnov test shows that the two samples are statistically indistinguishable: SN hosts appear to be drawn from the same population as field galaxies with respect to clustering in their environment.

Zoom In Zoom Out Reset image size

Let us now turn to the most clustered environments, by defining a significance limit (Σ_X%) to isolate the top 10%, 5%, and 1% most significant galaxy environments—the high significance group (HSG). Figure 1 shows the HSG cutoffs for Σ_10% as an example; actually the HSG is determined for each diameter D and each Deep field separately, then the HSGs for all are fields combined for a given D. We use summed Poisson probabilities to compare the number of SNe Ia in the HSG (N_obs) to the number expected (N_exp), which is the sum of the expected number of SNe Ia in each HSG galaxy (from Section 2.4). The Poisson probability of observing x = N_obs given μ = N_exp is expressed by Equation (2) (Bevington & Robinson 2003), and the summed Poisson probabilities for x > μ and x < μ are given in Equations (3) and (4), respectively,

$$\begin{equation} P_P(x;\mu) = \mu ^{x} \frac{e^{-\mu }}{x!} \end{equation} \tag{ 2 }$$

$$\begin{equation} P_{\rm SUM}(x,\infty ; \mu) = \sum _{x^{\prime }=x,x+1,\ldots }^{x^{\prime }=\infty } P_P(x^{\prime };\mu) \end{equation} \tag{ 3 }$$

$$\begin{equation} P_{\rm SUM}(0,x; \mu) = \sum _{x^{\prime }=0,1,\ldots }^{x^{\prime }=x-1} P_P(x^{\prime };\mu). \end{equation} \tag{ 4 }$$

As expressed by the morphology–density relation, galaxy clusters are dominated by early-type galaxies (Postman & Geller 1984); so Poisson probabilities are also calculated for the subset of early-type field galaxies and SNe Ia hosts in the HSG. Results for a representative sample of environment diameters in Table 2 show the number of HSG SN Ia to be consistent with expectations of the two-component model over a range of D and Σ_X%. Thus we conclude that this clustering parametrization method does not show an influence of clustering on SN Ia events. Neither including the SNe Ia outliers rejected in Section 2.4, nor increasing the environment redshift depth to ±2σ(1 + z), affects this conclusion.

Here we identify SNe Ia and galaxies in grade A clusters from the Olsen et al. (2007) cluster catalog. We use Poisson probabilities (Section 4.1) and a direct calculation of SNe Ia rates in clusters (Section 4.2) to look for an influence of clustering on the SN Ia rate per unit mass. As the SNLS detection efficiencies of Neill et al. (2006) are valid for 0.2 < z < 0.6, we restrict cluster, galaxy, and SN Ia redshifts to this range to use of them. This decreases the catalogs to 30 clusters, 70,587 galaxies, and 109 SNe Ia. We note Olsen et al. (2007) and Ilbert et al. (2006) use different Terapix data releases (T0002 and T0003 respectively), and the release used by Olsen et al. has more masked regions. However, the differences in field effective areas are ≲10%, so likely only ≲3 clusters of Ilbert catalog galaxies are missing from the Olsen catalog.

SNe Ia and galaxy members of clusters are identified as are neighbors in the environment of a galaxy in Section 3, except the volume is centered on the cluster coordinates. Since the cluster filter used by Olsen et al. (2007) has a profile with a core radius of r_c = 0.133h⁻¹₇₅ Mpc and a cut-off radius of r_co = 1.33h⁻¹₇₅ Mpc, results for 0.4, 0.8, and 1.5 Mpc will be presented as representative. For galaxies a redshift depth of $\pm 2 \sqrt{ (\sigma _{\Delta z/(1+z_{\rm SN})})^2 + (\sigma _{\Delta z / (1+z_{\rm VVDS})})^2 }\,(1+z_C)$ is used, a convolution of uncertainties in cluster redshifts from Section 2.3 and galaxy redshifts from Section 2.4. As SNe Ia have spectroscopic redshifts, a redshift depth of simply $\pm 2\sigma _{\Delta z / (1+z_{\rm VVDS})}$ is appropriate. The images in Figure 2 and data in Table 3 present six SNe Ia identified in Olsen clusters. While the three SNe Ia within D = 0.8 Mpc are probably physically associated with the clusters, this cannot be said for the remaining three. The number of field SNe Ia with 0.2 < z_SN < 0.6 predict ∼1.8 SNe Ia would randomly appear in the regions between r = 0.4 and r = 0.75 Mpc and $\pm 2\sigma _{\Delta z / (1+z_{\rm VVDS})}$. The probabilities of all three being random and all three not being random associates are both <20%. As it remains likely that at least one is physically associated with a cluster, we include them in our results, but remind the reader that interloping SNe Ia (and galaxies) will add to the uncertainties for D = 1.5 Mpc.

Zoom In Zoom Out Reset image size

Table 3.  Cluster SNe Ia Details

SN Ia SNLS ID	SN Ia R.A.	SN Ia Decl.	SN Ia zspec	SN Ia stretch	Host type	Host MV	Host offset	Cluster zphot	Cluster offset
03D1ax	02h24m2332	−04°43'1441	0.496	...	ES/0	−23.64	1.97''	0.53	10.8''
06D1kg	02h24m3257	−04°15'020	0.323	1.21	Sbc	−20.31	1.69''	0.30	47.2''
05D1by	02h24m3545	−04°12'042	0.299	0.99	Sbc	−21.17	0.86''	0.30	138.6''
04D1pg	02h27m0416	−04°10'314	0.515	1.05	Sbc	−19.62	0.18''	0.51	85.2''
05D3mq	14h19m0040	+52°23'0681	0.246	0.90	ES/0	−21.85	4.94''	0.25	9.99''
07D3af	14h19m0501	+53°06'0898	0.356	0.98	Scd	−18.61	0.35''	0.30	128.7''

Download table as:  ASCIITypeset image

4.1. Summed Poisson Probabilities

4.2. SN Ia Rates in Clusters

Here we use detection efficiencies from Monte Carlo simulations of the SNLS SN Ia identification pipeline from Neill et al. (2006) to directly calculate the SN Ia rate per unit mass in clusters, and compare it to that for the field. The corrected number of SN Ia which exploded in a given field in a year, N_corr,Ia, is extracted from Equation (3) of Neill et al. (2006). As shown in Equation (5), N_Ia is the total number of supernova observed in a given field, S is the number of observing seasons, _yr is the detection efficiency per year (the probability of a supernova being detected, sent for spectroscopy, and identified as a type Ia), and C_SPEC accounts for the fraction of SNe Ia for which spectra are obtained yet remain unidentified. [1 + 〈z〉_V] corrects for time dilation at the volume-weighted average redshift of the survey, and 〈z〉_V = 0.46. Detection efficiencies from Neill et al. (2006) and the number of observing seasons for each field up to 2007 January are in Table 5. Approximations to Poisson uncertainty from Gehrels (1986) determine the upper and lower limits on N_Ia at the 0.84 confidence level (corresponding to 1σ), which are substituted into Equation (5) to determine ΔN_corr,Ia:

$$\begin{equation} N_{{\rm corr},{\rm Ia}} = \frac{N_{\rm Ia}/S}{\epsilon _{yr} C_{\rm SPEC}} [1+\langle z\rangle _V]. \end{equation} \tag{ 5 }$$

Table 5.  Parameter Values for Equation (5)

Field	Seasons	yra	CSPECa
D1	4.0	0.3	0.94
D2	4.0	0.22	0.88
D3	4.0	0.31	0.80
D4	4.1	0.31	0.69

Note. From Neill et al (2006).

Download table as:  ASCIITypeset image

Table 6 contains the resulting corrected SN Ia rate per unit mass per year in clusters and the field. With only three identified cluster SNe Ia, statistical uncertainties dominate this calculation; systematics, mainly the error in galaxy mass calculations, are likely another ∼30%. Thus, our SN Ia rate is consistent with both the rate in early-type galaxies, 5.3 ± 1.1 × 10⁻¹⁴ SNe yr⁻¹ M⁻¹_☉ (Sullivan et al. 2006a), and the low-redshift cluster rate from WOOTS, 9.8^+5.9_−3.9 ± 0.9 × 10⁻¹⁴ SNe yr⁻¹ M⁻¹_☉ (Sharon et al. 2007).

Table 6.  Corrected SNe Ia Rates Per Unit Mass for D1–4

Galaxy set	NIa	Ncorr,Ia (SNe yr−1)	Stellar mass (×1014 M☉)	SN Ia rate (×10−14 SNe yr−1 M−1☉)
Clusters, 0.4 Mpc	2	2.8+6.4−1.6	0.33	8.3+19.4−4.9
Clusters, 0.8 Mpc	3	4.1+6.7−2.1	0.48	8.5+14.0−4.3
Clusters, 1.5 Mpc	6	8.1+7.3−3.1	0.78	10.4+9.4−4.0
Whole field	109	169.1+19.8−16.3	11.4	14.8+1.7−1.4
For Early-Type Galaxies Only
Clusters, 0.4 Mpc	2	2.8+6.4−1.6	0.29	9.6+22.4−5.6
Clusters, 0.8 Mpc	2	2.8+6.4−1.6	0.38	7.2+16.8−4.2
Clusters, 1.5 Mpc	2	2.8+6.4−1.6	0.56	5.0+11.6−2.9
Whole field	23	35.1+11.0−7.2	6.23	5.6+1.8−1.2
For the Brightest Early-Type Galaxies Only
Clusters, 0.4 Mpc	1	1.3+6.1−1.1	0.13	9.8+45.9−8.1
Clusters, 0.8 Mpc	1	1.3+6.1−1.1	0.15	8.7+40.9−7.2
Clusters, 1.5 Mpc	1	1.3+6.1−1.1	0.19	7.0+33.0−5.8
Whole field	2	2.6+6.3−1.7	1.02	2.5+6.2−1.6

Download table as:  ASCIITypeset image

There are two factors not considered which could affect SN Ia detection efficiencies in cluster galaxies. First, SN Ia detection efficiencies decrease in brighter hosts (Neill et al. 2006), and the brightest galaxies are early-type. Second, the SN Ia detection efficiency decreases for fainter, lower stretch SN Ia, and these faint SN Ia occur preferentially in early-type hosts (Sullivan et al. 2006a). Since cluster galaxies are predominantly early-type, both of these effects dominate in clusters: the first effect decreases the number expected in clusters by ∼15%, but quantifying the second would require more detailed completeness simulations. Both effects would cause us to underestimate the rate of SNe Ia in clusters relative to the field.

4.3. SN Ia Rates in E/S0 Cluster Galaxies

4.4. Effects of Altering Data Constraints

Type Ia supernova, galaxy, and cluster catalogs generated from the first four years of CFHT SNLS Deep survey data were combined to search for an influence of clustering on the SN Ia rate per unit mass. To avoid cluster-specific detection efficiencies and the inclusion of interloping galaxies as cluster members, we also considered subsets of regular and BCG-like early-type galaxies only. Results are dominated by the statistical uncertainties in identifying only three probable and three possible cluster SNe Ia, and consistent with the results of low-redshift cluster SNe Ia rate studies. To capitalize on SNLS's inclusion of both field and cluster environments, we used the continuous clustering strength parameter "significance" to compare the SN Ia rate per unit mass in and out of clustered environments, but did not find evidence of a clustering influence on the SN Ia rate per unit mass. Future work includes incorporating existing radio and infrared catalogs to investigate the rates of SNLS SNe Ia in radio loud and infrared luminous galaxies, and the VIRMOS spectroscopic redshifts for Deep field galaxies to explore the SNe Ia rate in small groups.

We gratefully acknowledge the CFHT Queued Service Observations team, Olivier Ilbert and Henry McCracken for early access to and correspondence regarding their photometric redshift galaxy catalog, Lisbeth Olsen for early access the optical cluster catalog, Jon Willis and Dan Maoz for helpful conversations, and our anonymous referee for constructive correspondence. This paper is based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the CFHT, which is operated by the National Research Council of Canada, the Institut National des Science de l'Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. This paper is also based on spectroscopic observations obtained at the Gemini Observatory which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership; the Very Large Telescope at the European Southern Observatory in Paranal, Chile; the W. M. Keck Observatory which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration; and the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile. This work is based in part on data products from the Canadian Astronomy Data Centre as part of the CFHT Legacy Survey, a collaborative project of NRC and CNRS. This work has been supported by NSERC and the University of Victoria.

Facilities: CFHT.