Bump Morphology of the CMAGIC Diagram

2025-04-27 0 0 3.25MB 15 页 10玖币

侵权投诉

L. Aldoroty

, L. Wang

, P. Hoeﬂich

, J. Yang

, N. Suntzeff

, G. Aldering

, P. Antilogus

, C. Aragon

3,5

S. Bailey

, C. Baltay

, S. Bongard

, K. Boone

3,7,8

, C. Buton

, Y. Copin

, S. Dixon

3,7

, D. Fouchez

E. Gangler

9,11

, R. Gupta

, B. Hayden

3,12

, Mitchell Karmen

,A.G.Kim

, M. Kowalski

13,14

, D. Küsters

7,14

P.-F. Léget

, F. Mondon

, J. Nordin

3,13

, R. Pain

, E. Pecontal

, R. Pereira

, S. Perlmutter

3,7

, K. A. Ponder

D. Rabinowitz

, M. Rigault

, D. Rubin

3,16

, K. Runge

, C. Saunders

3,7,17,18

, G. Smadja

, N. Suzuki

3,19

, C. Tao

10,20

R. C. Thomas

3,21

, and M. Vincenzi

3,22

George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Department of Physics and Astronomy, Texas A&M University, College

Station, TX, 77843, USA; laldoroty@tamu.edu

Department of Physics, Florida State University, Tallahassee, Fl, 32306, USA

Physics Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA, 94720, USA

Laboratoire de Physique Nucléaire et des Hautes Energies, CNRS/IN2P3, Sorbonne Université, Université de Paris, 4 place Jussieu, 75005 Paris, France

College of Engineering, University of Washington 371 Loew Hall, Seattle, WA, 98195, USA

Department of Physics, Yale University, New Haven, CT, 06250-8121, USA

Department of Physics, University of California Berkeley, 366 LeConte Hall MC 7300, Berkeley, CA, 94720-7300, USA

DIRAC Institute, Department of Astronomy, University of Washington, 3910 15th Avenue NE, Seattle, WA, 98195, USA

Univ Lyon, Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, F-69622, Villeurbanne, France

Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France

Université Clermont Auvergne, CNRS/IN2P3, Laboratoire de Physique de Clermont, F-63000 Clermont-Ferrand, France

Space Telescope Science Institute, 3700 San Martin Drive Baltimore, MD, 21218, USA

Institut für Physik, Humboldt-Universitat zu Berlin, Newtonstr. 15, D-12489 Berlin, Germany

DESY, D-15735 Zeuthen, Germany

Centre de Recherche Astronomique de Lyon, Université Lyon 1, 9 Avenue Charles André, 69561 Saint Genis Laval Cedex, France

Department of Physics and Astronomy, University of Hawai‘i, 2505 Correa Road, Honolulu, HI, 96822, USA

Princeton University, Department of Astrophysics, 4 Ivy Lane, Princeton, NJ, 08544, USA

Sorbonne Universités, Institut Lagrange de Paris (ILP), 98 bis Boulevard Arago, 75014 Paris, France

Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo Institutes for Advanced Study, The University of Tokyo, 5-1-5

Kashiwanoha, Kashiwa, Chiba 277-8583, Japan

Tsinghua Center for Astrophysics, Tsinghua University, Beijing 100084, People’s Republic of China

Computational Cosmology Center, Computational Research Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA, 94720, USA

Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 3FX, UK

Received 2022 October 3; revised 2022 December 16; accepted 2022 December 19; published 2023 April 27

Abstract

We apply the color–magnitude intercept calibration method (CMAGIC)to the Nearby Supernova Factory SNe Ia

spectrophotometric data set. The currently existing CMAGIC parameters are the slope and intercept of a straight

line ﬁt to the linear region in the color–magnitude diagram, which occurs over a span of approximately 30 days

after maximum brightness. We deﬁne a new parameter, ω

, the size of the “bump”feature near maximum

brightness for arbitrary ﬁlters Xand Y.Weﬁnd a signiﬁcant correlation between the slope of the linear region, β

in the CMAGIC diagram and ω

. These results may be used to our advantage, as they are less affected by

extinction than parameters deﬁned as a function of time. Additionally, ω

is computed independently of templates.

We ﬁnd that current empirical templates are successful at reproducing the features described in this work,

particularly SALT3, which correctly exhibits the negative correlation between slope and “bump”size seen in our

data. In 1D simulations, we show that the correlation between the size of the “bump”feature and β

can be

understood as a result of chemical mixing due to large-scale Rayleigh–Taylor instabilities.

Uniﬁed Astronomy Thesaurus concepts: Supernovae (1668);Type Ia supernovae (1728);Photometry (1234);

Spectrophotometry (1556)

1. Introduction

Type Ia supernovae (SNe Ia)are important to cosmology

(Riess et al. 1998; Perlmutter et al. 1999)because they may be

used to determine luminosity distances to their host galaxies

due to the predictability of their light curves (Pskovskii 1967;

Phillips 1993; Riess et al. 1996; Goldhaber et al. 2001). Due to

this predictability, photometric data from SNe Ia are standar-

dizable for cosmological studies.

Several successful methods have been developed to quantify

SNe Ia light curves, including the decline rate Δm

and stretch

parameters (Pskovskii 1967; Phillips 1993; Perlmutter et al.

1997; Guy et al. 2005,2007; Burns et al. 2014; Kenworthy

et al. 2021). Statistical methods have also been used, including

functional principal component analysis (He et al. 2018). These

models can be improved if additional information is considered

(Wang et al. 2009; Foley & Kasen 2011; Rose et al. 2021).

Correcting for the effects of dust extinction and reddening is

a key part of calibrating SNe Ia, as it has signiﬁcant

cosmological consequences. As light from the SN passes

through its host galaxy dust, the dust interferes and selectively

removes more blue than red light. A similar effect occurs when

The Astrophysical Journal, 948:10 (15pp), 2023 May 1 https://doi.org/10.3847/1538-4357/acad78

Original content from this work may be used under the terms

of the Creative Commons Attribution 4.0 licence. Any further

distribution of this work must maintain attribution to the author(s)and the title

of the work, journal citation and DOI.

the light traverses the Milky Way. Although Galactic dust

reddening is generally well-measured (Schlaﬂy & Finkbeiner

2011), it is more difﬁcult to quantify the effects of dust from

other galaxies. Further, as more SNe Ia are discovered, their

diversity becomes more apparent, and disentangling extra-

galactic dust reddening from intrinsic color variation becomes

more important. Theoretically, Hoeﬂich et al. (2017)showed

that the mass and metallicity of the progenitor white dwarf

(WD)can affect the intrinsic color of SNe Ia by as much as

0.1 mag in (B−V). Therefore, it is necessary to establish

robust, reddening-free color parameters for SNe Ia.

The color evolution of SNe Ia has been observed to be

similar across different events and thus has been used to

estimate host galaxy extinction (Lira 1995; Phillips et al. 1999).

Wang et al. (2003)introduced the color–magnitude intercept

calibration (CMAGIC)method as a way to utilize data taken in

the month after maximum brightness in order to standardize

SNe Ia. About one week after maximum brightness, the color–

magnitude diagram (hereafter “CMAGIC diagram”)for

normal-bright SNe Ia (i.e., neither subluminous nor over-

luminous)displays a remarkably linear relationship in the rest-

frame Bmagnitude versus B−V,B−R, and B−Icolors,

which lasts for two to three weeks. The slope of this region,

, is independent from other measurable quantities. We can

use this property to calibrate SNe Ia accurately and

independently of other methods, with sensitivity to different

systematic sources of error. It is interesting to explore

CMAGIC because in the future, we may be able to use

CMAGIC to calibrate SNe Ia lacking data around maximum

light. Further, it has been shown that CMAGIC curves may be

useful in helping to break the degeneracy between intrinsic

color and reddening (Hoeﬂich et al. 2017). Conley et al. (2006)

shows that cosmological results from CMAGIC are consistent

with the current picture of cosmology, i.e., an accelerating ﬂat

universe with a cosmological constant. Similarly, Wang et al.

(2006)shows that CMAGIC methods have a Hubble residual

rms deviation of approximately 0.14 mag, comparable to

methods that use the maximum brightness B

max

Wang et al. (2003)notes two different morphologies found

in the CMAGIC diagram—one with a luminosity excess

around the time of maximum brightness (the “bump”feature),

and one without. The authors also note a bifurcation in slope

distribution, which they suggest may be indicative of two

progenitor channels. Chen et al. (2021)also observed a varying

slope in color curves, creating a proxy for the color–stretch

parameter s

(Burns et al. 2014). Conley et al. (2006)discuss

the “bump”feature in more detail, stating that the probability of

a“bump”occurring increases as B-band stretch increases;

however, it is still possible to ﬁnd SNe with the same stretch

where one has a “bump”and the other does not. They ﬁnd that

SNe with stretch values of s>1.1 have a bump, and none with

s<0.8 have one. Those with 1.0 <s<1.1 have a 50%

probability of having a bump, and SNe with 0.8 <s<1.0 have

an approximately 8% chance of having a bump. Wang et al.

(2006)notes that the difference between B

max

and the

CMAGIC parameter B

is directly tied to the existence of a

bump, and therefore may be an important consideration for

color corrections. The CMAGIC method has also been applied

to derive distances and dust reddenings of some well-observed

SNe Ia (Wang et al. 2020; Yang et al. 2020).

Hoeﬂich et al. (2017)note that CMAGIC is useful for

studying the intrinsic physical properties of SNe Ia because the

locations of its distinguishing features are affected by the

central density of the progenitors and the explosion scenario,

and propose that variations in the slope may also point toward

underlying SN physics. If the shape of the CMAGIC diagram

points toward physics, and some SNe show a “bump”feature

where others do not, it is important to quantify this shape

variation because it may enhance our understanding of the

intrinsic colors of SNe Ia.

In this paper we present empirical relations as well as

theoretical results of the CMAGIC diagram, centered around

the “bump”feature. In Section 2.1, we describe the Nearby

Supernova Factory (SNfactory; Aldering et al. 2002)data set

used in this work. In Section 2.2, we describe the functional

principal component analysis (fPCA)light-curve ﬁtting based

on the results of He et al. (2018). Section 2.3 describes the

spectral analysis procedures. Section 2.4 describes the ﬁtting

procedures, as well as deﬁning one useful “bump”parameter,

. Results and discussion of the study are in Section 3. First,

we discuss the “bump”morphology in Section 3.1, followed by

theory based on the 1D Hoeﬂich et al. (2017)model 23,

modiﬁed to include mixing. Section 3.3 contains CMAGIC

diagrams of light-curve templates, including those from the

fPCA method (He et al. 2018), SNooPy (Burns et al. 2011),

and SALT3 (Kenworthy et al. 2021). We vary the templates’

parameters in order to reproduce the morphology identiﬁed in

the data. We show that all three sets of templates are successful

at reproducing the “bump”(or lack thereof). Finally, the results

are summarized in Section 4.

2. Method

2.1. Data

Spectra from SNfactory (Aldering et al. 2002)were used for

this analysis. Details about the SNfactory data set and data

reduction can be found in Saunders et al. (2018)and Aldering

et al. (2020). After correcting the observed spectra to the rest-

frame, synthetic photometry for each SN was made using BVRI

ﬁlters from Bessell & Murphy (2012), which were calibrated to

the Vega system using alpha_lyr_stis_010.fits from

the CALSPEC database (Bohlin et al. 2014)(see Appendix A).

These ﬁlters were chosen for ease of comparison to Wang et al.

(2003). The zero-point for SNfactory data is kept hidden, thus,

all magnitudes in this work are the calculated magnitude plus a

constant. Cuts were then applied to the data, requiring that

observations exist before maximum light, and that a minimum

of three observations exist in the linear region in all three types

of CMAGIC diagram (see Section 2.4).

We do not explicitly remove peculiar SNe Ia. This work

includes a total of 85 SNe, where there are 31 in the “bump”

group, 34 in the “no bump”group, and 20 in the “ambiguous”

group.

2.2. fPCA Fitting

Light curves are ﬁt using fPCA, as described by He et al.

(2018).

It is advantageous to use PCA methods to ﬁt complex

curves, such as light curves, because the result is a

parameterization of the curve that is a linear combination of

orthogonal PC functions. Therefore, it is straightforward to

propagate the errors (See Appendix B). The ﬁtted light curves

These templates can be used via snlcpy (Aldoroty et al. 2022), located at

https://github.com/laldoroty/snlcpy.

The Astrophysical Journal, 948:10 (15pp), 2023 May 1 Aldoroty et al.

are used to determine the location of the brightest point in the B

band, as well as the change in magnitude between peak Bband

brightness and 15 days later, Δm

15,B

. We use the ﬁts from the

light curves to compute the CMAGIC diagram for each SN and

color combination. For this analysis, only the ﬁrst two B- and

V-band speciﬁc PC components from He et al. (2018)are used

because these describe the majority of the variation in the light

curves, and we found that including the third and fourth

components resulted in unphysical ﬁts for some SNe because

the data were insufﬁcient to constrain the ﬁt realistically using

this method.

2.3. Spectral Analysis

Pseudo-equivalent widths (pEWs), i.e., the depths of spectral

features given a pseudo-continuum drawn around an individual

feature, are calculated for all SNe using the data spectrum

nearest to maximum brightness available in the Bband.

Gaussian ﬁts were applied to the λ6355 and λ5972 Si II lines

using a bootstrapping method. Two regions, each 20 Åwide,

were identiﬁed around either side of each absorption line, and

endpoints were randomly drawn 225 times from these regions

to determine the continuum for normalization. The ﬁnal pEW is

the area integrated under the Gaussian ﬁt, and the error is the

standard deviation of each set of area measurements. This

method mirrors the procedure used by Galbany et al. (2015).

pEW is used as a parameter for statistical tests in Table 1, and

is shown in Figure 3.

2.4. CMAGIC

The CMAGIC diagram of an SN Ia shows its evolution in

brightness as a function of color (Figure 1). After explosion, the

SN grows brighter and bluer in optical wavelengths. At

maximum brightness, it starts to redden linearly as it dims over

the next ∼30 days, before turning around and becoming

linearly bluer as it continues to dim. Some SNe Ia show a small

luminosity excess around maximum brightness (Figure 1, left),

where others do not (Figure 1, right). We refer to this

luminosity excess as the “bump”feature. In this section, we

discuss the methodology used to handle the two linear regions

in the CMAGIC diagram, followed by quantifying the size of

the “bump”feature.

2.4.1. Linear Regions

Wang et al. (2003)found that there are two linear regions

that occur shortly after maximum brightness in the CMAGIC

diagram; the ﬁrst begins 5–10 days after maximum, and ends at

roughly 30 days. The second begins at around 40 days (shown

in the left panel of Figure 1), although discussion of this region

is outside the scope of this study. To ﬁt the ﬁrst linear region

(hereafter “linear region”)of the Bversus B−V,B−R, and

B−ICMAGIC diagrams for each SN, we used Levenberg–

Marquardt least squares minimization via mpfit in Python

(Moré 1978; Moré & Wright 1993; Markwardt 2009;

Koposov 2017). The ﬁts were performed such that χ

was

ﬁxed to equal the number of degrees of freedom via scaling the

errors, with different scalings for the two linear regions. The

endpoints of the linear regions in the CMAGIC diagrams for all

SNe were determined by visual inspection.

SNe with fewer than three observations in the linear region

of any of the three diagrams (B−V,B−R,orB−I)were

excluded, in order to allow for a minimum of one degree of

freedom in all linear ﬁts.

2.4.2. Quantifying the Size of the “Bump”Feature

The size of the “bump”was quantiﬁed by identifying the

B−Vcolor corresponding to B-band maximum brightness.

Then, the CMAGIC diagram was normalized by the linear ﬁt.

The “bump”size is deﬁned as

(( ) ) ()wb=-+-BV B m ,1

BV BV BVmax 0 Bmax

where m

Bmax

is the magnitude at maximum brightness in the

Bband, β

is the slope of the linear region from the ﬁt(purple

line in Figure 1),

(

)-BV

max is the color at the time of B-band

maximum, and B

BV0

is the value of the ﬁt line when

(B−V)=0. If there is a bump, ω

will be positive; if there

is no bump, the value will be negative. Error propagation for

is described in Appendix C.

3. Results and Discussion

3.1. “Bump”Morphology

SNe are distinguishable in the CMAGIC diagram by the

presence, or lack, of a luminosity excess relative to the linear

region near B

max

, the maximum magnitude in the Bband. We

have qualitatively divided our sample into three categories

based on visual inspection: those with a bump, those without a

bump, and those where it is ambiguous whether or not there is a

bump. The last group includes those without enough data in

this region to say deﬁnitively if there is a “bump”or not, and

Table 1

Results for a Two-sample KS Test (D

n,m

)and Independent Two-sample t-test

for the Parameters Presented in This Work, Based on the “Bump”vs. “No

Bump”Samples

Parameter D

n,m

pDnm,tp

Δm

15,B

0.544 7.40 ×10

−5

−3.74 3.89 ×10

−4

Δm

15,V

/Δm

15,B

0.64 9.56 ×10

−7

6.30 3.25 ×10

−8

pEW Si II λ6355 0.55 4.18 ×10

−5

−3.01 3.70 ×10

−3

pEW Si II λ5972 0.49 4.07 ×10

−4

−4.77 1.12 ×10

−5

0.75 2.40 ×10

−9

−6.63 8.94 ×10

−9

0.43 2.96 ×10

−3

−3.62 5.89 ×10

−4

0.44 2.60 ×10

−3

−3.45 2.60 ×10

−3

0.94 1.22 ×10

−15

11.61 2.69 ×10

−17

0.62 2.03 ×10

−6

5.13 3.01 ×10

−6

0.57 2.31 ×10

−5

4.98 5.20 ×10

−5

Note. We correct for the “look-elsewhere effect”by dividing our signiﬁcance

level α=0.05 by the number of parameters in this table. Thus, our signiﬁcance

level is α

=0.005. The ﬁrst section shows the results for parameters

independent of the bump. The second section shows the results for slope β

the linear region of the CMAGIC diagram, which we have shown to be

strongly correlated with “bump”size (Figure 2). The third section shows results

for “bump”size ω

. The functions ks_2samp() and ttest_ind() from

scipy.stats were used. The ﬁrst column lists the tested parameter; the

second and fourth columns show the test statistics; the third and ﬁfth columns

show the p-values for the test statistics in the columns to their left. For the

Kolmogorov–Smirnov (KS)test, the null hypothesis is that the “bump”and “no

bump”samples are drawn from the same distribution. No assumption is made

about the distributions of the data. The two-sample t-test checks the null

hypothesis that the mean value of the two groups is identical. This test assumes

the data are normally distributed. We do not assume equal variance. We are

able to reject the null hypothesis for all parameters.

The Astrophysical Journal, 948:10 (15pp), 2023 May 1 Aldoroty et al.

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

BumpMorphologyoftheCMAGICDiagramL.Aldoroty1,L.Wang1,P.Hoeﬂich2,J.Yang1,N.Suntzeff1,G.Aldering3,P.Antilogus4,C.Aragon3,5,S.Bailey3,C.Baltay6,S.Bongard4,K.Boone3,7,8,C.Buton9,Y.Copin9,S.Dixon3,7,D.Fouchez10,E.Gangler9,11,R.Gupta3,B.Hayden3,12,MitchellKarmen3,A.G.Kim3,M.Kowalski13,14,D.Küsters7,14,P.-F...

展开>> 收起<<

Bump Morphology of the CMAGIC Diagram.pdf

共15页,预览3页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Bump Morphology of the CMAGIC Diagram

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: