New directions
in strong lensing
Masamune Oguri
RESCEU/Physics/Kavli IPMU
University of Tokyo

2019/8/23 CosmoCruise@Sea

Reference − arXiv:1907.06830
Strong gravitational lensing of explosive transients

30v1 [astro-ph.CO] 16 Jul 2019

Masamune Oguri1,2,3
1 Research Center for the Early Universe, University of Tokyo, Tokyo 113-0033,

Japan
2 Department of Physics, University of Tokyo, Tokyo 113-0033, Japan
3 Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU,
WPI), University of Tokyo, Chiba 277-8582, Japan
E-mail: masamune.oguri@ipmu.jp
Abstract. Recent rapid progress in time domain surveys makes it possible todetect various types of explosive transients in the Universe in large numbers,some of which will be gravitationally lensed into multiple images. Althougha large number of strongly lensed distant galaxies and quasars have alreadybeen discovered, strong lensing of explosive transients opens up new applications,
including improved measurements of cosmological parameters, powerful probesof small scale structure of the Universe, and new observational tests of dark
matter scenarios, thanks to their rapidly evolving light curves as well as theircompact sizes. In particular, the compactness of these transient events indicatesthat the wave optics e↵ect plays an important role in some cases, which can leadto totally new applications of these lensing events. Recently we have witnessed
first discoveries of strongly lensed supernovae, and strong lensing events of othertypes of explosive transients such as gamma-ray bursts, fast radio bursts, andgravitational waves from compact binary mergers are expected to be observed
soon. In this review article, we summarize the current state of research on strong
gravitational lensing of explosive transients and discuss future prospects.

Keywords: cosmology, gravitational lensing, transients

Strong gravitational lenses• multiply imaged, highly magnified• many applications− cosmology− dark matter distribution− distant/faint sources− resolving fine structure

lensed quasar (SQLS)

lensed galaxy (SLACS)

observerlenssource• galaxy• cluster• quasar• galaxyobserverlenssource• galaxy• cluster• quasar• galaxy
• SN
• GRB
• FRB
• GW

•…

Strong lensing of explosive transients?

• supernova (SN)

PS1-10afx, SN Refsdal, iPTF16geu• gamma-ray burst (GRB)
not yet• fast radio burst (FRB)
not yet• gravitational wave (GW)
not yetQuimby, MO+ Science 344(2014)396

PS1-10afx
lensing galaxy[OII] at z=1.117

lightcurve

SN host[OII] atz=1.388

spectrum• Type Ia supernova magnified by a factor of 30!
• multiple images were not resolved

Kelly+ Science 347(2015)1123

SN Refsdal• core-collapse SN
strongly lensed
by a cluster

SY• 4 images S1-S4
discovered in2015 October

SX

HST image• 2 more images
S1-S4

predicted• SX : 2016-2017• SY : <2005Kelly+ ApJ 819(2016)L8“Reappearance” of Refsdal
Kelly et al.

SX/S1 flux ratio

al Letters, 819:L8 (6pp), 2016 March 1

Figure 2. Comparison between the predicted and the actual position of image SX of SN Refsdal. Coordinate published predictions are ove
F125W and F160W difference images made by subtracting the 2015 December 11 exposures from archival template images taken in 2011
the angular offsets between the measured positions of multiply imaged sources and their positions in the best-ﬁtting respective models. Th
et al. (2016), and Grillo et al. (2015) predictions are all consistent with the measured position of image SX within the reported rms scatte
Diego et al. (2016) model was not published and is 0. 6 (J. Diego 2015, private communication).

~350 daysen the predicted and the actual position of image SX of SN Refsdal. Coordinate published predictions are overplotted on the coaddition ofe images made by subtracting the 2015 December 11 exposures from archival template images taken in 2011. The circles show the rms of
Figure3. Simultaneous
constraintson etthedelay
and magniﬁcation of image SX relative to image S1 from photometry of image SX
he measured positions of multiply imaged sources and their positions in thebest-ﬁtting
respective models.
The Diegoal.time(2016),
Jauzacshow
the 68%
and 95%conﬁdence(2015) predictions are all consistent with the measured position of imagedimensional
SX within thecontours
reported rms
scatter.
The residual
scatter
for the levels, and model predictions plot 68% conﬁdence levels. Since many of th
as not published and is 0. 6 (J. Diego 2015, private communication). Gaussian distributed, the 68% limits do not imply that they are necessarily inconsistent with the measurements. Except for the Jauzac e

SX-S1 time delay• image SX appeared exactly at the predictedrefer to models presented by Treu et al. (2016). While all other plotted predictions were made in advance of the HST Cycle 23 observation
30, “Post Blind Zitrin-c” and “Post Blind Jauzac” were updates made at a later date. “Post Blind Zitrin-c” is an update of the “Zitrin-g”
was left to be freely weighted to assure that its critical curves pass between the four Einstein cross images. For “Post Blind Jauzac,” theposition for images S1–S4 in the source plane and recompute the time delays analytically using their LENSTOOL model of the cluster potedelay, the earlier the 2015 December 11 observations are in the light curve of SX. The black dashed line marks the delay beyond which w
of SN Refsdal. We extrapolate to earlier epochs using the best-ﬁtting second-order polynomials.

position and time!

• fully blind test of cluster mass models∼10 days for a year-long delay). Furthermore, the uncertainties
are typically highly non-Gaussian, so the 95% conﬁdence
interval is not simply twice as wide as the 68% one.
5. CONCLUSIONS

the reappearance here shows the ppredictions using models of the distribut
clusters and the general theory of relabrightness of light from SN Refsd
approximately in agreement with predfor most models, unknown systematic uGoobar+ Science 356(2017)291

iPFT16geu• Type Ia supernova magnified
by a factor of 52!

• 4 images separated by ~0.6″• time delays are predicted to
be short, <1 day~0.6″
HST imageAdvantages?

• simple and fast light curves• standardizable candles• wave effect?

Advantages?

• simple and fast light curves• standardizable candles• wave effect?

Simple and fast light curves• simple light curves with a rise and fall (SN,
GRB, FRB) or theoretical templates (GW)

time scales, month (SN) or sec-msec• short(GRB, FRB, GW)• robust and accurate measurements oftime delays!

time delay Δt

Light curves of explosive transients
20

2

month

GRB 120703A

count [arbitrary units]SNabsolute magnitude

Ia

18

16

30

0

30

60

sec
− msec090

10days after peak brightness
15

GRB

1

0

10

time since BAT trigger time [sec]FRB 121102

GW150914

1.0

strain [10 21]

msec

S/N

FRB

10

5

0

GW

0.5

msec

0.0
0.5
1.0

20

10

0

time [msec]

10

20

0.25

0.30

0.35

time [sec]

0.40

0.45

Time delays for quasar lenses
Tewes et al.: COSMOGRAIL XIII – Time delays of RX J1131 1231

• quasar light
curves arestochastic• monitoringfor years
required• precision of~1 day at
mostFig. 4. Optical monitoring of RX J1131 1231, as obtained from deconvolution photometry. From top to bottom are shown the RTewes+2013
band light curves for the quasar images A, B, C, and D along with the 1 photometric error bars. Colors encode the contributing
instruments. Curves B and D have been shifted by +0.3 magnitudes for display purposes. The light curves are available in tabularImproved time delays• improved constraints on H0(see also Ken Wong’s talk!)• probing dark matter substructures• probing compact dark matter

Improved constraints on H0• improved measurement errors on Δt(~day → up to ~msec!)• better use of a lensed host galaxy
w/ SN
imagesw/o SN
imagessimulated by glafic

e.g., MO 2007; Keeton & Moustakas 2009; Liao+2018

Substructure and time delays
3

1

Δt=
0.72
day

0

1

1

2

2

3

3

2

1

0

✓1 [arcsec]

1

2

3

Δt=
0.65
day

0

1

3

108M⊙
subhalocritical curves
images2✓2 [arcsec]✓2 [arcsec]nosubhalocritical curves
images

2

3

3

2

1

0

✓1 [arcsec]

12• substructure affect Δt, especially small ones
• can be easily detected by lensed GRB, FRB, GW

3

Searching for echo signals• time delay for a point

flux

mass lensM
Δt ∼ 0.02 msec (1 + zl)( M⊙ )• ~msec transients (e.g. FRB)
can constrain compact dark
matter with M ≳ 30 M⊙ bysearching for echo signals(e.g., Munoz+2016)

Δt

time

Advantages?

• simple and fast light curves• standardizable candles• wave effect?

Type Ia supernovae• correlation between peak luminosities andwidth of light curves• standardizable candle to measure DL(z)(from LBL website)

Gamma-ray bursts– 77 –• several relations to measure DL(z) proposed
Eiso-Epeak (Amati+2002)
Lpeak-Epeak (Yonetoku+2004)
Eγ-Epeak (Ghirlanda+2004)…

Log(E!)

52

51

50

Schaefer 2007

49
1

2

Log[Epeak(1+z)]

3

4

Gravitational waves• direct measurements of DL(z) from inspiral02 (2016)

compact binaries (standard siren)
PHYSICAL REVIEW LETTERSe, thestrain
events have a combined signal-to) of 24 [45].
5/3
O detectors were observingzat the time of
2/3
e Virgo detector was being upgraded,hough not sufficiently sensitive to detect
L observationals operating but not inly two detectors the source position ismined by the relative arrivaland5/3time11/3
area of approximately z
600 deg2 (90%[39,46].
atures of GW150914 point to it beinge coalescencechirpof twoblack holes—i.e.,
massfrequency
ral and merger, and subsequent final black
Over 0.2 s, the signal increases in frequency
about 8 cycles from 35 to 150 Hz, where
eaches a maximum. The most plausible

week ending
12 FEBRUARY 2016

M
h/
f
D (z)

f˙ / Mf

Abbott+2016

Strongly lensed standardizable candle• direct measurement of magnification factor μ• precious info that breaks various degeneraciesmag
2.5 log μzinserts a constant mass sheet ext . Importantly, tBartelmann
MNRAS
296(1998)763
However,
there Kolattis (e.g.,a &fundamental
difficultyin themass
distribution[79]).
transform also changes time delays (13) between a
However,
therewhich
is a fundamental
difficultyinstrong lensing
analysis,originates fromvariousmultiple image
pairs asBreaking
mass-sheet
degeneracy

strong lensing
analysis,originates One
from suchvario
degeneracies
inherent
to the whichlens equation.
degeneracies
inherent
to
the
lens
equation.
Onesu
exampleis the mass-sheet
degeneracy
[80],
in
which
the
tij ! (1 ext ) tij ,(exampleis mathematicallythe mass-sheet
degeneracy[80], in which
followingtransform
is considered
exact degeneracy,transform
isconsideredΦ whichfollowing
indicatesthatH
estimatedfrom2 observed ti
image positions
unchanged
0✓
delay should(✓)
scalesHext(1 + ext, 0✓.2 Therefo(24)! (1as 0 )!(✓)ext )H
2ext ,
(
(✓)
!
(1

)
(✓)
+

ext
H0 measured from time delays is subject
to2
lens potential•

uncertainty of ext that cannot be constrained fr! (1 ext ) ,(25)strong lensingsource
observations.
As
we
will
discuss
lat
!
(1

)
,
(
ext
positionwherewayexttois constant.
It degeneracy
is straightforward
toobserve
see that
one
break
the
is
to
where ext is constant. It is straightforward to see ththis transform factor
keeps
the
lens equation(1) unchanged.
measurementofμbreaksmagnificationµ,becausethetransformchan
this transform keeps the lens equation (1) unchangThistransform
corresponds
toan
operationthat
thisdegeneracyµas Thistransform corresponds to an operation th2
rescales
the
mass
of
the
lensing
objectandinsteadrescales the massof theext
lensingµ ! (1) µ.object and inste(•

insertsaconstant
mass
sheet

.
Importantly,
this
ext
2
inserts
κextθ /2 (1−κext)Φa constant mass sheet ext . Importantly, t
Note
that
this
transform
does
notchangetheratiotransform
alsochanges
time
delays(13)
betweenanyatransform also changes time delays (13) betweenMO & Kawano MNRAS 338(2003)L25

Breaking slope-H0 degeneracy

dimensionless Hubble constant h=H0/100km/s/Mpc

tational lens time delays for distant supernovae

w/o μ

L3

• H0 from time delays

vs radial density slope• approx. degeneracy
w/ μ

due to mass-sheet
degeneracy• measurement of μ
break degeneracy

radial slope β [ρ(r) ∝ rβ−3]

Advantages?

• simple and fast light curves• standardizable candles• wave effect?

e.g., Schneider+1992; Nakamura & Deguchi 1999

Wave optics effect• in most cases, we can safely assume geometric
optics for calculating lensing effects• geometric optics is λ→0 limit approximationof wave optics that is more fundamental• wave optics effect can play an important rolein some cases

Wave vs. geometric optics
wave optics ψ ∝ d θ e∫2observer2πifΔt(θ)

lenssourcearrival time Δt(𝛉)geometric optics ∇θ Δt(θ) = 0(Fermat’s principle)

Wave effect: Diffraction• when λ ≫ Rlens wave propagation is not affectedby the lens

• no magnification, µ ~ 1
observerlenssourceRlens~GMEin/c2
wavelength λWave effect: Interference• when λ ≲ Rlens multiple light ray paths interfere• magnification oscillates as a function of source
position and wavelength

observerinterference

lenssourceRlens~GMEin/c2
wavelength λMagnification in wave optics• parameter w

Strong lensing of explosive transientsmagnification µ

8

geom.
w = 0.1
w =1
w = 102 / Ein = 0.15

6

to the di↵raction, where w is defined in eq
On the other hand, when w & 1, the glensing magnification exhibits oscillating bfunction of the source position or the wav
which can be observed only when the sogravitational
satisfies the condition given
by equation (lens
radius 4.4.
discuss specific examples in Section

controls wave effect
w∼

4

R

λ

wavelength

3. Explosive transients• diffraction

2

3.1. Supernovae

at w ≪ 1

0

3

2

1

0

1

2

3

1 / Einβ1

Figure 5. The magnification factor for a point mass lens in wave
optics, which is computed from 2equation (43), as a function of
the source position. Here we fix 2 /✓Ein = 0.15 and change 1
Ein factor change as a a function of
to see how the magnification
the source position, for w = 0.1 (dash-dotted magenta), 1 (thickβθA supernova is an explosion associated wi
of a star. Observations of supernovae
history, for example some supernovae took
Milky Way were observed even in the na
were recorded in the literature. Here we pr
overview of supernovae. Interested readers
to reviews (e.g., [138]) and textbooks (e.gmore details.
Observationally there is a great deal
in properties of supernovae, including their• interference
at w ≳ 1

Finite source size effectmagnification µ

8

geom.
w = 102 /✓Ein = 0.15

6

~1/w

4

2

0

3

2

1

0
1 /✓Ein1

2• source needs to becompact to observe
interference patternθEin
βsrc ≲
w
Rlens
w∼
λ
3
• at λ→0 we recovergeometric optics

Can we observe wave effect?
21

10

1/ ˆs = Dos Ein/Rs

Einstein radius/source size

105
4

no lensing
due todiffraction

interference

wave effectmay beobserved

wave optics

103
diff

102

t
ren

e

M

geometric optics

no interference

wave effectis neverobserved

101
100
nt
e
r
e
diff

10 1
10 2 210

M

no lensing due tofinite source size

10 1

100

101

gravitational radius/wavelength w

102

103

104

105

Can we observe wave effect?

Strong lensing of explosive transients
1014

FRB

no wave effect

SN

1010

Rs [km]source size

1012

108

GRB

106
104

GW

102
100 4 2 0 2 4 6 8 10 12 14 16 18 20 22
10 10 10 10 10 10 10 10 10 10 10 10 10 10

f [Hz] frequency

can
of ga
Time
imag
in m
posit
Secti
appli
colla
stand
we c
break
equa
This

Can we observe wave effect?
• gravitational waves (LIGO band)

point mass lens w/ Mlens ~102 M⨀ (Nakamura 1998)
subhalo lensing w/ MEin ~102 M⨀ (Dai+2018)
microlensing in high µ region (Diego+2019)• gravitational waves (LISA band)galaxy lens w/ MEin~107 M⨀ (Takahashi+2003)• fast radio bursts

point mass lens w/ Mlens ≳10-5 M⨀ (Zheng+2004)

Can we observe wave effect?
VOLUME 80, NUMBER 6•

non—diffract
cally
very
inte
gravitational waves (LIGO band)
The author
3
M. Sasaki for⨀ (Nakamura 1998)
lens
for valuable c(Dai+2018)
tality of Yuka
the substantia(Diego+2019)
work is supp
istry of Educa(4125).
gravitational waves (LISA band)

point mass lens w/ M ~10 M
subhalo lensing
microlensing in high µ region
signal-to-noise ratio•

PHYSICAL REVIEW LETT

galaxy lens w/ MEin~107 M⨀ (Takahashi+2003)• fast radio bursts[1] A. Abram
review, K
by S. W.
Press, Cam-5 ⨀ (Zheng+2004)[2] For examp
42, 1123[3] E. S. Phin
T. Piran, aNakamura 1998
[4] D. Markopoint mass lens w/ Mlens ≳10 M
frequencyFuture detectability?

• supernova (SN)

PS1-10afx, SN Refsdal, iPTF16geu• gamma-ray burst (GRB)
not yet• fast radio burst (FRB)
not yet• gravitational wave (GW)
not yet10 1Strong lensing probability• steep function ofredshift at low-z

Psl(zs)10 2• to observe strong

Psl(zs)10 3

lensing events:

10 4
10 5

reach out to z~O(1)10 6

detect O(103) events

10 7
0.1

1

redshift zs

10• GRB, FRB, GW

satisfy these criteriain near futureProperties of first SN lens events
nameredshift
PS1-10afx 1.388
SN Refsdal 1.49
iPTF16geu 0.409

µtot
~31
~74
~52

θmax

<0.4″
32″
~0.6″

discovery
surveytargetedsurvey• galaxy-scale lenses for those discovered inwide-field surveys• magnifications tend to be high, µtot ≳ 30

Selection effect• at low-z, strong lensing probability is a steep
function of redshift• higher chance of observing highly magnified
high-z events than moderately magnified
low-z events• therefore, in shallow surveys (zlim ≲ 1),

we tend to observe highly magnified strong
lens events(→ first discoveries of lensed FRB, GW?)

MO MNRAS 480(2018)3842
M. Oguri

Example: lensed GWs• advanced LIGO

• Cosmic Explorer. Distributions of time delays and magnifications for pairs of multiple images from the mock strong lens catalogues. As in Fig. 12, w
Pop-I/II model from 3000 years and 1 year observations for advanced LIGO (left) and Cosmic Explorer (right), respectively. The upper
ys and magnifications of leading (filled circles) and trailing (crosses) images for any image pairs in the mock catalogues. The bottoms and ratios of magnifications of leading and trailing images.

highly magnified pairpairs with modest µ
eventswithΔtobservatories≲ 1dayand models of binary
andΔt ~R 10-100
days
Summary of predicted
event rates
for various
BH mergers.
denotes the total
number of obs
obs

Rsl is the total number of strongly lensed events per year, ⟨µsl ⟩ is the median magnification of strongly lensed events, Rpair is the tot
multiple
image ofpairs
peryear, and!t is
the median timedelayofofmultiple
the observed⟨µcatalogues.
the medianleading /µtrailing
Distributions
time
delaysmagnifications
for pairs
imagesmultiple
from theimage
mockpairs,
strongandlensAs⟩inis Fig.
12, weSummary• strong lensing of explosive transientsis next frontier!

− very accurate Δt for better constraints
on cosmology and small-scale structure− make use of standardizable candle nature− possibility of observing wave effect• first discoveries coming soon
• for more details, see arXiv:1907.06830