Supernovaeand the IFU

Ryan Foley University of Illinoisand Dan Scolnic University of Chicago

WFIRST-AFTA White PaperR ≈ 100 IFU Spectrograph0.6 ≤ λ ≤ 2 µm

7 Epochs of IFU Spectroscopy at S/N = 31 Epoch Near Max at S/N = 101 Epoch at Late Times at S/N = 65-day cadence4.2 Months for Spectroscopy

No mention of selection, false positives, or ifS/N is peak/median/other

Our SimulationsStart with WFC3 IR Grism for SensitivityScale To Match Total Time in White Paper

Assume Peak S/NAdd Appropriate Noise

Determine Recovery Rate (∆z < 0.05, >80% SN Ia Match, Best Match)

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Observed Wavelength (µm)

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tive

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z = 0.2

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R = 50R = 70

R = 100R = 130R = 150

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Recov

eredResolution Matters for Classification

S/N = 50S/N = 20S/N = 10S/N = 3

0.0 0.5 1.0 1.5Redshift

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eredS/N REALLY Matters for Classification

z = 1.5 S/N = 3

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z = 1.5S/N = 20

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S/N = 50S/N = 20S/N = 10S/N = 3

S/N Matters for MISclassification

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S/N Matters for MISclassification

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S/N REALLY Matters for Classification

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S/N = 3

S/N REALLY Matters for Classification

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red

Convolved with Redshift Distribution

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RelaxedStrict

Samples of SNe Ia have Low RV

RV =AV/E(B-V)

ï0.1

0.00.1

0.20.3

0.4Me

asured

E(Bï

V) (ma

g)

ï0.4

ï0.20.00.20.40.60.81.0

AV (mag)

R V = 3.1

R V = 2.2

Foley & Kasen 2011

4000 4500 5000 5500 6000 6500 7000Rest Wavelength (Å)

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ux +

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stan

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Optical Spectrum to Measure Velocity

High Velocity

Low Velocity

Silicon

Measure Silicon Velocity

5900 6000 6100 6200 6300Rest Wavelength (Å)

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tHigh Velocity:~ -13,000 km s-1

Low Velocity:~ -10,000 km s-1

Wider Lines WithHigher Velocity

Intrinsic Color Depends on SN Velocity

Foley & Kasen 2011

ï0.1

0.00.1

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0.4Me

asured

E(Bï

V) (ma

g)

ï0.4

ï0.20.00.20.40.60.81.0

AV (mag)

HighïV

elocity

SNe Ia

LowïV

elocity

SNe Ia

R V = 2.5

R V = 2.2

High VelocityLow Velocity

RV =AV/E(B-V)

Large Biases from Intrinsic Color

Mandel, Foley, & Kirshner 2014

20

−16

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Linear versus Constant Mean Intrinsic Color

Si II v

elecity

(103 km

/s)

−0.12 −0.08 −0.04 0 0.04 0.080

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Numb

er of S

N Ia

Change in AV Extinction Estimate

Fig. 21.— The change the individual extinction estimates, ∆AV ,as a function of ejecta velocity, from the Gaussian (constant meanintrinsic color) model to the Linear model. This quantifies theerror in AV incurred by ignoring velocity information. At highabsolute ejecta velocities, the Gaussian model underestimates theintrinsic colors (too blue), and overestimates AV . Hence, the cor-rection to AV is as negative as −0.11 mag. At low absolute veloc-ities, the Gaussian model overestimates the intrinsic colors (toored), leading to corrections as positive as +0.06 mag.

routine (Appendix B).In Figure 21, we compare the extinction estimates ob-

tained from the linear model (§4.3) to those from theGaussian model ( §4.2). For each model, we computethe posterior marginal mode of P (As

V |{Os, vs},Model)for each SN s, and we show differences∆As

V in the modesbetween Gaussian and Linear. At high absolute ve-locities, |v| > 11, 800 km s−1, the extinction estimateunder Linear is a smaller positive number than underGaussian, because the intrinsic colors at high ejecta ve-locity are inferred to be redder under the the Linearmodel. The∆As

V estimates quantify the systematic errorin the extinction estimate incurred by ignoring velocityinformation. While most of the ∆AV estimates clustersaround zero, at high ejecta velocities the extinction cor-rection is as negative as ∆AV ≈ −0.11 mag, while at lowejecta velocities it is as positive as∆AV ≈ 0.06 mag. The(mean, median) ∆AV of the sample are (−0.013,−0.006)mag.In Figure 22, we show the change in the extinction es-

timates, ∆AV , from switching from the Gaussian in-trinsic color model to the Step model. Because thestep function model infers a redder mean intrinsic colorfor high velocity events, the extinction estimates forhigh velocity events are shifted to smaller positive num-bers. The mean intrinsic color for normal velocity events(|v| < 11, 800 km s−1), however, is bluer than the globalmean intrinsic color using Gaussian model, so the ex-tinction estimates are larger positive numbers. At highSi II ejecta velocities, the extinction corrections have adistribution peaked near ∆AV ∼ −0.08 mag, whereasat normal velocities, they have a distribution clusteredaround +0.02 mag. The extinction correction is as nega-tive as −0.11 mag or as positive as 0.04 mag. The (mean,median) ∆AV of the sample are (−0.024, 0.001) mag.The extinction AV estimates within each model are

sensitive to the assumed value of RV controlling the dust

−16

−14

−12

−10

Step Function versus Constant Mean Intrinsic Color

Si II v

elecity

(103 km

/s)

−0.12 −0.08 −0.04 0 0.040

10

20

30

Numb

er of S

N Ia

Change in AV Extinction Estimate

Fig. 22.— The change in the individual extinction estimates,∆AV , as a function of velocity, from the Gaussian (constant meanintrinsic color) model to the step function model. This quanti-fies the error in AV incurred by ignoring velocity information. Athigh absolute ejecta velocities, the Gaussian model underestimatesthe intrinsic colors (too blue), and overestimates AV . Hence, thecorrection to AV is as negative as −0.12 mag. At low absolutevelocities, the Gaussian model overestimates the intrinsic colors(too red), leading to corrections as positive as +0.04 mag.

reddening law. Regardless of the model (Gaussian, Lin-ear, or Step), the average AV extinction was foundto be τ̂ = (0.25 ± 03, 0.35 ± 0.04, 0.40 ± 0.05) mag forRV = (1.7, 2.5, 3.1), respectively. Hence, a typical ex-tinction value will increase by a factor ≈ 1.14 going fromRV = 2.5 to RV = 3.1, or decrease by a factor of ≈ 0.71going from RV = 2.5 to RV = 1.7. These factors arenot exactly equal to the ratios of the assumed RV val-ues because SN Ia spectra differ from stellar spectra andthe dust extinction AV estimates rely not just on B− Vcolors but also use information from B − R and B − Icolors.

5. CONCLUSION

We have constructed a hierarchical Bayesian model toestimate the relation between the peak intrinsic colors ofSN Ia and their ejecta velocities measured from Si II spec-tral lines. We model the distribution of the observed ap-parent colors, conditional on the velocity measurement,as a probabilistic combination of the intrinsic color lo-cus, a dust reddening distribution and measurement er-ror scatter. The hyperparameters of the underlying dis-tributions are determined from the posterior density con-ditional on all the SN Ia data. Bayesian inference withthe hierarchical model can be thought of as a probabilis-tic deconvolution of the data into the different sourcesof randomness generating it. We developed and imple-mented a Gibbs sampling code (Appendix B) to gener-ate MCMC samples from the global posterior density ofthe unknowns conditional on the data. The deviance in-formation criterion (DIC) (Appendix C) is computed toevaluate the relative fits of models with different levelsof complexity. We have used this model to analyze adataset of 79 nearby SN Ia with BV RI light curves andSi II spectroscopic ejecta velocity measurements.The empirical distribution of Si II ejecta velocities (Fig.

11) is well described by a gamma distribution with a long

R ≥ 100 improves recovery rate, gives moreprecise (less biased) distances, and allowsfor additional systematic tests

S/N > 20 needed for robust classification

Spectroscopy from Ground?Could do everything at z < 1 withdedicated 8-m telescope

Distances through imaging withsingle high-S/N spectrum?

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