No LIGO MACHO -...

No LIGO MACHOPrimordial Black Holes in Light of Supernova Lensing

Miguel Zumalacarregui

Rencontres de Moriond Cosmology - March 2018

with Uros Seljak (1712.02240)

Miguel Zumalacarregui (Berkeley) PHBs in Light of SNe Lensing

Warning: slopes ahead!

(but not that many black holes)


Gravitational Waves vs ΛCDM

DE models& gravity theories

ruled out(Ezquiaga’s talk)

MACHO/PBH?(this session)

100Ωbh2 = 2.222± 0.023 (1.0%)

Ωch2 = 0.1197± 0.0022 (1.8%)

ΩΛ = 0.685± 0.013 (1.9%)

Planck ’15 (T+lowP only!)


LIGO MACHO miracle?

10−18 10−15 10−12 10−9 10−6 10−3 100 103

MPBH [M]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

α≡

ΩP

BH/Ω

M(9

5%c.

l.)

HS

C

WM

APfe

mto

-len

sin

g

Kep

ler

Haw

kin

gra

dia

tion

FIR

AS

MA

CH

O

ER

OS

Eri

dan

osII

Wh

ite

Bin

arie

s

LIG

OB

Hs

SNe lensing → MZ & Seljak ’17

(adapted from Ezquiaga+ ’17 Reviews: Carr+ ’16, Sasaki+ ’18)Miguel Zumalacarregui (Berkeley) PHBs in Light of SNe Lensing

LIGO MACHO miracle?

10−5 10−3 10−1 101 103 105

MPBH [M]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

α≡

ΩP

BH/Ω

M(9

5%c.

l.)

WM

AP

FIR

AS

MA

CH

O

ER

OS

Eri

dan

osII

Wh

ite

Bin

arie

s

LIG

OB

Hs


(adapted from Ezquiaga+ ’17 Reviews: Carr+ ’16, Sasaki+ ’18)


LIGO MACHO miracle?

10−5 10−3 10−1 101 103 105

MPBH [M]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

α≡

ΩP

BH/Ω

M(9

5%c.

l.)

WM

AP

FIR

AS

MA

CH

O

ER

OS

Eri

dan

osII

Wh

ite

Bin

arie

s

SN

ele

nsin

g(t

his

wor

k)

LIG

OB

Hs


(adapted from Ezquiaga+ ’17 Reviews: Carr+ ’16, Sasaki+ ’18)


No LIGO MACHO?

ligar (verb)

1. Bind, connnect.

2. [Colloquial] Flirt.

(yo) ligo → I flirt

macho (noun)

1. Male.

2. [Colloquial] Dude, bro.

No LIGO MACHO

my love life sucks, bro

LIGO Lo(g)-normalMACHO

mine’s normal, bro

(→ from Garcia-Bellido+ ’17)


Lensing by compact objects (Rauch ’91, Seljak & Holz ’99, Metcalf & Silk ’06)

D(z,∆µ) =D(z)√1 + ∆µ

Distance (perceived)Magnification

?S1

?S2

halo

−0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

∆µ - magnification (wrt FRW)

10−2

10−1

100

101

102

Pro

babi

lity

Emptybeam

Magnificationtail ∝ µ−3

P (µ, z, α) at z = 0.8

α = 0 (no PBH)

α = 0.84 (all PBH)

PBH signatures:

slight demagnification (most sources)highly magnified events (few sources)

→ Different & complementary to stellar microlensing (Moniez’s Talk)


Lensing by compact objects (Rauch ’91, Seljak & Holz ’99, Metcalf & Silk ’06)

D(z,∆µ) =D(z)√1 + ∆µ

Distance (perceived)Magnification

?S1

?S2

•BH

−0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6


10−2

10−1

100

101

102

Pro

babi

lity

Emptybeam


P (µ, z, α) at z = 0.8

α = 0 (no PBH)

α = 0.84 (all PBH)

PBH signatures:

slight demagnification (most sources)highly magnified events (few sources)

→ Different & complementary to stellar microlensing (Moniez’s Talk)


SNe Magnification (MZ & Seljak ’17)

−0.6 −0.4 −0.2 0.0 0.2 0.4 0.60.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

z = 1.2

PL(µ; z, α) convolved with Gaussian σ = 0.15

−0.6 −0.4 −0.2 0.0 0.2 0.4 0.60.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

z = 0.7

−0.6 −0.4 −0.2 0.0 0.2 0.4 0.6

∆µ (0.15/σµ)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

z = 0.2

α = 0.0

α = 1.0



−0.6 −0.4 −0.2 0.0 0.2 0.4 0.60.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

z ∈ [0.90, 1.5]

Nunion = 48

NJLA = 34

z = 1.2

−0.6 −0.4 −0.2 0.0 0.2 0.4 0.60.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

z ∈ [0.50, 0.9]

Nunion = 119

NJLA = 151

z = 0.7

−0.6 −0.4 −0.2 0.0 0.2 0.4 0.6

∆µ (0.15/σµ)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

z ∈ [0.00, 0.5]

Nunion = 412

NJLA = 555

z = 0.2

α = 0.0

α = 1.0

JLA

Union



−0.6 −0.4 −0.2 0.0 0.2 0.4 0.60.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

z ∈ [0.90, 1.5]

Nunion = 48

NJLA = 34

z = 1.2

−0.6 −0.4 −0.2 0.0 0.2 0.4 0.60.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

z ∈ [0.50, 0.9]

Nunion = 119

NJLA = 151

z = 0.7

−0.6 −0.4 −0.2 0.0 0.2 0.4 0.6

∆µ (0.15/σµ)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

z ∈ [0.00, 0.5]

Nunion = 412

NJLA = 555

z = 0.2

α = 0.0

α = 1.0

JLA

Union

−0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.010−1

100

101

3σ 5σ

z = 1.2Total NSNe

Cumulative

−0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.010−1

100

101

102z = 0.7

−0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0

∆µ × (0.15/σµ)

10−1

100

101

102

103

z = 0.2

α = 0.0

α = 1.0

JLA

Union


Results

Parameters:

α =

ΩPBH

ΩM

mean m

dispersion correctionσ2i = σ2obs,i+k2−σ2lens

Skewness k3

Kurtosis k4

Not shown:

ΩM (Planck+BAO)

standardization (JLA) 0.2 0.4 0.6 0.8

α (PBH)

−0.8

0.0

0.8

1.6

2.4

100k

2

−0.8

0.0

0.8

1.6

k3

−0.2

0.0

0.2

0.4

k4

−0.16 −0.08 0.00 0.08

m

0.2

0.4

0.6

0.8

α(P

BH

)

−0.8 0.0 0.8 1.6 2.4

100 k2

−0.8 0.0 0.8 1.6

k3

−0.2 0.0 0.2 0.4

k4

JLA

Union 2.1

xi =1

σi(mob,i −mth(zi, µ)− m)

PSNe = N(

1 + erf

(k3x√

2

))× exp

(−1

2|x|2−k4

)

α <

0.346 (JLA)

0.405 (Union)(95%)


Highly-magnified events or peculiar SNe?

34

36

38

40

42

44

46

48

Dis

tan

cem

od

ulu

s(m

ag) 91b

Ia?NUV-R

91T

slow decline

↑ subluminous

↓ overluminous

Union 2.1

Outliers

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

z

−5.0

−2.5

0.0

2.5

5.0

7.5

∆m/σ

m

±3σ

Outliers in Union 2.1

4 overluminous → 3 peculiar

8 subluminous → 5 peculiar

Thanks to D. Rubin (sample) & Ll. Galbany (assesment)

→A

bso

lute

ma

gn

itu

de

→ Decline rate (mag, 15 days)

(Taubenberger ’17)

−0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6


10−2

10−1

100

101

102

Pro

babi

lity

Emptybeam


P (µ, z, α) at z = 0.8

α = 0 (no PBH)

α = 0.84 (all PBH)

−0.15 0.00 0.15 0.30 0.45 0.60

k4 (kurtosis)

0.00

0.15

0.30

0.45

0.60

0.75

0.90

α(P

BH

frac

tion

)

Union 2.1

+ all outliers

+ over-luminous


Source size vs Lens Mass

Errors/typos in Sec. IIC. New version coming ⇒ Basic results hold


Finite sources

Point lens + point source

µ =1

l

l2 + 2ξ2√l2 + 4ξ2

− 1

Finite source η ≡ RSξ

=source size

Einstein radius

µmax =√

1 + 4η−2 − 1

z-dependence

η(zL, zS) = η0

[DL

H0DSDLS

]1/2

η0 = 0.02h1/2

(RS

113AU

)(M

ML

)1/2

Optical depth 〈µ〉 = e2τ(zS) − 1

?S

•BH

ξ = 1

l

10−3 10−2 10−1 100 101

l/χ (impact parameter, normalized)

100

101

102

103

µ+

1(m

agni

fica

tion

)

µmax =√

1 + 4η−2 − 1

η ≡ RS/ξ

0

0.01

0.10

1.00


Finite sources


µ =1

l

l2 + 2ξ2√l2 + 4ξ2

− 1


=source size

Einstein radius

µmax =√

1 + 4η−2 − 1

z-dependence

η(zL, zS) = η0

[DL

H0DSDLS

]1/2

η0 = 0.02h1/2

(RS

113AU

)(M

ML

)1/2


?S

•BH

ξ = 1

l

η

10−3 10−2 10−1 100 101

l/χ (impact parameter, normalized)

100

101

102

103

µ+

1(m

agni

fica

tion

)

µmax =√

1 + 4η−2 − 1

η ≡ RS/ξ

0

0.01

0.10

1.00


Finite sources


µ =1

l

l2 + 2ξ2√l2 + 4ξ2

− 1


=source size

Einstein radius

µmax =√

1 + 4η−2 − 1

z-dependence

η(zL, zS) = η0

[DL

H0DSDLS

]1/2

η0 = 0.02h1/2

(RS

113AU

)(M

ML

)1/2


?S

•BH

ξ = 1

l

η

0.0 0.2 0.4 0.6 0.8 1.0

zL

0.00

0.05

0.10

dτ/dz L

10−1

100

101

µm

ax

zS = 1.0, RS = 113AUη0 = 0.1, M ≈ 3 · 10−2

η0 = 0.5, M ≈ 1 · 10−3

η0 =

1.0, M ≈3 · 10 −4µ(zS) = 0.14


Finite source magnification PDF (MZ & Seljak in prep.)

0.0 0.2 0.4 0.6 0.8 1.0

zL

0.00

0.05

0.10

dτ/dz L

10−1

100

101

µm

ax

zS = 1.0, RS = 113AUη0 = 0.1, M ≈ 3 · 10−2

η0 = 0.5, M ≈ 1 · 10−3

η0 =

1.0, M ≈3 · 10 −4µ(zS) = 0.14

Results valid for M & 0.01MDemagnification peak ∆µ ∼ −µ

indistinguishable w. noise X

Magnification tail (∆µ & 1)

outlier fraction to ∆µ ∼ 0.5 X

Base analysis was conservative:

M ∼ 10−4 half way to LSS!

−0.15 −0.10 −0.05 0.00 0.05 0.10 0.15 0.20

∆µ

0

5

10

15

20

25

30

35

PL(∆µ

;zS,η

0)

zS = 1.0, σµ = 0

η0 = 0 (Fit), M →∞η0 = 0.1, M ≈ 3 · 10−2

η0 = 0.5, M ≈ 1 · 10−3

η0 = 1.0, M ≈ 3 · 10−4

α = 0 (pure LSS)

0.0 0.5 1.0 1.5 2.0 2.5

∆µ

10−3

10−2

10−1

100

Cum

ulat

ive

PL

+no

ise zS = 1.0, σµ = 0.15

η0 = 0

η0 = 0.1η0 = 0.5

η0 =

1.0LSS


Conclusion: No LIGO MACHO

10−4 10−3 10−2 10−1 100 101 102 103 104

MPBH [M]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

α≡

ΩP

BH/Ω

M(9

5%c.

l.)

LIG

OB

Hs

EROS

Eri

dan

osII

SNe lensing(this work)

Pla

nck

(col

l)

Pla

nck

(ph

oto)

0.0 0.5 1.0 1.5 2.0 2.5

∆µ

10−3

10−2

10−1

100

Cum

ulat

ive

PL

+no

ise zS = 1.0, σµ = 0.15

η0 = 0

η0 = 0.1η0 = 0.5

η0 =

1.0LSS

−0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0

∆µ × (0.15/σµ)

100

101

102

NSNe

z ∈ [0.50, 1.5]

Nunion = 167

NJLA = 185

3σ 5σ

α = 0.0

α = 1.0

JLA

Union

ΩPBH

ΩM< 0.35 (95% c.l. JLA)

100% DM excluded at 4.9σ!

Finite SNe → M & 0.01M

Complementarity &agreement w. other probes

Robust against outliers,cosmology, correlated noise


Gravitational Waves vs ΛCDM

(some of) LIGO BHscould be primordial,

but subdominant DM

LIGO could rule out ΛCDM(confirming high H0 tension)

2000 2005 2010 2015 2020year

62.5

65.0

67.5

70.0

72.5

75.0

77.5

80.0

82.5

H0 [

km/s

/Mpc

]

KPSH0ES

CPHSH0ES

GAIA + HST?

W1

W3 W5W7 W9

P13 P15 BAO P+S4

GW170817

15 x BNS

Dist. Ladder CDM Std. Sirens

MZ in prep.

Thanks!


Backup Slides

10−4 10−3 10−2 10−1 100 101 102 103 104

MPBH [M]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9α≡

ΩP

BH/Ω

M(9

5%c.

l.)

LIG

OB

Hs

EROS

Eri

dan

osII

SNe lensing(this work)

Pla

nck

(col

l)

Pla

nck

(ph

oto)


Base magnification PDF + LSS

Fit to simulations (Rauch ’91)

P = A

[1− e−µ/δ

(µ+ 1)2 − 1

]3/2(if µ > 0)

A, δ → normalize & 〈µ〉 = µFRW(z)

- Dependence P (µ, µ) only

- Universal (point lens/source)

−0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

∆µ (relative to FRW mean)

10−1

100

101

PL(µ,z,α

)atz

=1

PBH fraction

α = 0

α = 0.30

α = 0.60

α = 0.85

Adding LSS: (Seljak & Holz ’99)

PL(µ; z, α) =

∫ µ1−α

0dµ′PLSS(µ′, z)PC [µ− µ′(1− α)︸︷︷︸

smooth contrib

, αµ′︸︷︷︸mean

]

PLSS → Turbo GL (Marra & Paakkonen ’12)Miguel Zumalacarregui (Berkeley) PHBs in Light of SNe Lensing

SNe population

mth = 5 log10(DL(z)

)− 2.5 log10(1 + ∆µ) + 25

Li(~θ, α) =

∫dµPL(∆µ; zi, α)PSNe(mi, σi, zi,mth, ~θ)

SNe distribution

xi =1

σi(mob,i −mth(zi,∆µ)− m)

σ2i = σ2ob,i + k2 − σ2L(z)

PSNe(x) = N(

1 + erf

(k3x√

2

))exp

(−1

2|x|2−k4

)

θ ⊃ mean (m), intrinsic scatter (k2), skewness (k3), kurtosis (k4),

standardization mob,i = m?B,i − (MB − αX1,i + βCi)


Cosmology Dependence

Assumed flat ΛCDM

Planck+BOSS: ΩM = 0.309± 0.006

(Alam+ ’17)

Weak effect of perturbations

SNe: σ8 = 1.07+0.50−0.76

(Macaulay+ ’17)

Degeneracy:

empty-beam shift ↔ expansion

No ΩM prior

- slightly weaker results

- “best” case PBH

Tension

α ≈ 0.8 → 3σ w. SNe

ΩM ≈ 0.36 → 8σ w. P+B

- Lack of outliers!

−0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6


10−2

10−1

100

101

102

Pro

babi

lity

Emptybeam


P (µ, z, α) at z = 0.8

α = 0 (no PBH)

α = 0.84 (all PBH)

0.250 0.275 0.300 0.325 0.350 0.375 0.400

ΩM

0.00

0.15

0.30

0.45

0.60

0.75

0.90

α(P

BH

)

JLA (no priors)

JLA (Planck+BAO)


Correlated noise

Assumed independent

Ltot =∏

i

Li

Use JLA simple covariance

∆m(zj) = γ1

3

∑

i

Cij√Cjj

i ∈ (26, 27, 28) connects low-high z

10−2 10−1 10010−2

10−1

100

−14

−12

−10

−8

−6

−4lo

g(|C

ij|)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

zj

0.00

0.02

0.04

0.06

0.08

0.10

∆m

full

diag. removed

Empty beam ∆m

−3 −2 −1 0 1 2 3

γ (SNe correlation)

0.00

0.15

0.30

0.45

0.60

0.75

0.90

α(P

BH

)

Non-diagonal

Non-diagonal +1


No LIGO MACHO -...

Documents

Transcript of No LIGO MACHO -...