超高増光率重力マイクロレンズ
大栗 真宗(東京大学 RESCEU/物理/Kavli IPMU)

2017/10/23 観測的宇宙論WS@弘前とが可能です。最近のブラックホール合体からの重力波の発見に触発され、宇宙のダーク
マターをブラックホールで説明する理論研究や、ブラックホールの存在量や質量を重力マ

重力マイクロレンズ

イクロレンズから観測的に制限する研究が再び活発になっています。

• 手前のコンパクト天体の重力レンズ効果による遠方の星の一時的な増光(Kavli IPMU news No. 38)

今回の話• 銀河団中心部で新しいタイプの変動天体を発見• 重力レンズで非常に大きく増光された単独の星と解釈 (増光率1000以上)• 観測からソースとレンズの性質、およびダーク
マターモデルへの制限可能性を議論する

Caustic-Crossing Event

Kelly, .., MO+, arXiv:1706.10279

Icarusの発見
Discovered
Discovered inin latelateApril
April“RefsdalRedux”“RefsdalRedux” program
program toto searchsearch forfor reappearance
reappearance

2011
2011
SN
SNRefsdal
RefsdalReappearance
Reappearance

5ʺ
5ʺ

F125W
F125W(J)(J)

Late
Late MayMay 2016
2016

Considered
Considered first
first byby (Jordi)(Jordi) Miralda-Escude
Miralda-Escude (1991)(1991)(銀河団MACSJ1149.5+2223@z=0.54)

Caustic-Crossing Event

Kelly, .., MO+, arXiv:1706.10279

Icarusの発見
Discovered
Discovered inin latelateApril
April“RefsdalRedux”“RefsdalRedux” program
program toto searchsearch forfor reappearance
reappearance
new transient

2011
2011
SN
SNRefsdal
RefsdalReappearance
Reappearance

5ʺ
5ʺ

F125W
F125W(J)(J)

Late
Late MayMay 2016
2016

Considered
Considered first
first byby (Jordi)(Jordi) Miralda-Escude
Miralda-Escude (1991)(1991)(銀河団MACSJ1149.5+2223@z=0.54)

Caustic-Crossing Event

Kelly, .., MO+, arXiv:1706.10279

Icarusの発見
Discovered
Discovered inin latelateApril
April“RefsdalRedux”“RefsdalRedux” program
program toto searchsearch forfor reappearance
reappearance
new transient

2011
2011
SN
SNRefsdal
RefsdalReappearance
Reappearance

5ʺ
5ʺ

F125W
F125W(J)(J)

Late
Late MayMay 2016
2016

Considered
Considered first
first byby (Jordi)(Jordi) Miralda-Escude
Miralda-Escude (1991)(1991)
Johan
Richard model(銀河団MACSJ1149.5+2223@z=0.54)

Kelly, .., MO+, arXiv:1706.10279

光度曲線
Flux (µJy)

0.2

2012
Spera15 (2

2016
Near Peak=184.6)

Spera15/3% PBH ( 2 =219.6)

26

0.1
27
0.0

54000

55000
56000
Date (MJD)

57000• 徐々に増加、急激な減光 (非対称)Magnitude (AB)2008

Kelly, .., MO+, arXiv:1706.10279

スペクトル
1000

Rest Wavelength (Å)
3000
4000
5000

2000

6000

0.08
Underlying Point Source
Flux Excess May 2016 (rescaled;

2

=1.5)

27

0.04

27.5
28

0.02
Model Stellar Spectra:
T =11180K log g=2 AV =0.02 mag MW

0.00

2

=16.3

T =12250K log g=4 AV =0.08 mag MW

2

=30.6

T =12375K log g=2 AV =0.08 mag SMC

2

=12.9

T =13591K log g=4 AV =0.13 mag SMC

2

=16.5

28.5
29
30

Magnitude (AB)

Flux (µJy)

0.06

0.02
2000

4000

6000

8000
10000
12000
Observer Wavelength (Å)

14000

16000

• 強いバルマーブレーク

Fig. 2: The SEDs of LS1 measured in 2013–2015 (red) and of the rescaled, excess flux
density at LS1’s position close to its May 2016 peak (Lev 2016A; black) are consistent.
Rescaling the SED of the flux excess to match to that of the 2013–2015 source yields‰2‹ = 1.5, indicating that they are statistically consistent with each other despite a flux
density difference of a factor of ≥ 3–4. The SED shows a strong Balmer break consistent
with the host-galaxy redshift of 1.49, and stellar atmosphere models (15 ) of a mid-to-lateB-type star provide a reasonable fit. Black circles show the expected flux density for eachmodel.

→ z=1.49 (=母銀河のz) のB型星

[これまでで再遠方の単独の星の観測]

さらに他のイベント
3

g from the Hubble Frontier Fields. The central panel
and infrared bands from HST. Two boxes within ther. These regions are shown as two inset panels on the), which are caused by the gravitational lensing of the2014

October 30 2016

January 3 2017

Lev 2017A

Lev 2016B

0.5″
LS1 / Lev 2016A

LS1 / Lev 2016A

LS1 / Lev 2016A

Fig. 4: Highly magnified stellar images located near the MACS J1149 galaxy cluster’s
CC. The left panel shows LS1 in 2014; we detected LS1 when it temporarily brightened bya factor of ≥ 3 in late-April 2016. The center panel shows the appearance of a new image
dubbed Lev 2016B on 30 October 2016. The red curve marks the location of the cluster’s
CC from the CATS cluster model (7 ). The position is consistent with the possibility that
it is a counterimage of LS1. The right panel shows candidate named Lev 2017A with≥ 4‡ significance detected on 3 January 2017. If a microlensing peak, Lev 2017A mustcorrespond to a different star.

↑ Icarus近傍での他のイベント(Kelly, .., MO+, arXiv:1706.10279)← 他の銀河団でも似たイベント(Rodney, .., MO+, arXiv:1707.02434)

焦線通過 (caustic crossing)
臨界曲線(critical curve)

焦線 (caustic)
星 (ソース)ソース平面

星 (イメージ)

星 (イメージ)

イメージ平面
明るさ• 焦線を通過する単独の星→ 非対称な光度曲線
時間simulated by glafic

普通のマイクロレンズの例

simulated by glafic

焦線通過 (caustic crossing) の例

巨大アーク内の焦線通過• Miralda-Escude (1991) が銀河団背後の重力レンズを受けた巨大アーク内の単独の星の焦線通過の観測可能性を議論• 滑らかな銀河団質量分布のみを考慮• しかしながらほんのわずかなコンパクト天体が存在するだけで焦線の構造が大幅に変更される(Diego, .., MO+ 2017;Venumadhav+ 2017)• たとえダークマター自体がなめらかであってもIntra-Cluster Light (ICL)の星がそのようなコンパ
クト天体の役割を担う

Intra-Cluster Light (ICL)• 銀河団内の広がった放射• DM分布に沿った分布• 銀河団内の銀河の外側から剥ぎ取られた星の放射に由来
NASA/ESA/IAC/HFF team, STScI

Diego, .., MO+, arXiv:1706.10281 (see also Venumadhav+ 2017)
f=0.003•

ICLの影響

f=0.01

Diego
et
al.
ICLによる臨界曲線の「破壊」

f=0.03

f=0
w/o
ICL
f=0.1

f=0.0003
f=1
w/ ICL

Microlenses near caustics

log10(µ) f=0.001

臨界曲線の破壊により•
s a function of microlenses surface mass density. Each panel shows the CC region when
0
5

平均増光率

10

2

4

6

8

nt. The 4case f = 1 corresponds
to the model of 増光率がサチる
Spera (2015) at the position off=0.003
Icarus.
w/o
ICL
The10
last panel in the bottom does not show the yellow line since it extends beyond thensity (i.e., smooth plus microlens) is the same in all panels.

103

コンパクト天体の存在•
narrow CC widens, with overlapping crit

f=0.01of the microcaustics
w/ ICLthat 2are notably lessform a complex
network (see, for instancを考慮することは
f=0.0310
with negative
parity.
-0.2
0.0
0.2 Fig. 8). This network extends up to a ma
Icarusの解釈に必須
not takeplace if there [arcsec]that depends
on the total number andf=0.1mas
臨界曲線からの距離
ince in that case thecrolenses. In the case of Fig. 6, this net
Fig. 9.— Median of the magnification as a function of distance toFig. 10.— Histograms of the magnification (image plane)
circularregionwould
well
beyonddisplayedof andview.
e main CC (negative distances mean they are measured toward
location theof the main
CC (black andfield
red curves)at two poT

MO, Diego, Kaiser, Kelly & Broadhurst, arXiv:1710.00148

焦線通過 (caustic crossing) を理解する• Icarusのような銀河団巨大アーク内の焦線通過
イベントはコンパクトDM (e.g., PBH) の有用なプローブになりうる• このような焦線通過観測からそのレンズとソースにたいしてどのような情報が得られるだろうか？

We
consider
a
point
mass
lens
in
a
constantcon
We
presentsome
keyresults
whiche.g., Chang & Refsdal (1979)
ssionsinthefollowing
sections.
gence
(κ̄)
and
shear
(γ̄)
field
which
comes
from
a
m
consider
a
point
mass
lens
in
a
constant
conversions in the following sections.
単純な解析モデル
we have(κ̄)lens
andmodel.
shearThen(γ̄) field
which comes from a macro

−1
odel.
Then
we
have
Lens equationµ M)= 1 − κ̄ − γ̄,
点質量レンズ (質量•tLens equation−1−11と−γ̄,
κ̄ + γ̄.
+ 一定の
shear
µtconvergence=µr1 −=κ̄ −(1
mass lens in a−1constant converµ
=
1
−
κ̄
+
γ̄.
(2
The
total
magnification
by
the
macro
lens
model
is
r
巨大アーク内の高増光率領域は)mass
field• lens
which
comes
from a convermacroinaconstant
1µt µr .µtWe
considera0region near the tangential crit
=
1
̄
¯
⇡
ave
otal
magnification
theamacrolens model is µ̄ =
field
which
comes
from
macro
−1 by
curve where µt ≈ 0 gives rise to the high magnificat
We
consideraregionnear
thetangential
criticave= 1The
−
κ̄
−
γ̄,
(1)
lens
equation
by
a
point
mass
lens
with
mass
点質量レンズの臨界曲線と焦線は
−1
•
where
µ
≈
0
gives
rise
to
the
high
magnificationtabsence
the
macro
mass
model,
hastheEins=in11−− κ̄κ̄と
+ γ̄,
γ̄.of
(2)
=lens
−
(1)
のために大幅に変更をうける
equation
by
a
point
mass
lens
with
mass
M
radius of=by1the−+ γ̄.macro(2) hasnence
lens modelµ̄ =ofκ̄macrothemassmodel,! is"1/2the Einstein
4GM
D
ls
egion
near
the
tangential
criticalofθE =model2 is µ̄ =
.
by
the
macro
lens
ves rise to the highc Dos
! magnification.
"D
ol
1/2
gion near the tangential criticalソース平面 (焦線)

イメージ平面 (臨界曲線), and their dependences on the lens and source prop!
"1/2
Dls
4 4GM
es. The result 正パリティ
is used to interpret
MACS
J1149
LS1
.
(μt>0)
負パリティ (μt<0) θE = c2 D Dplace constraints on the lens mass as well as theos olperty of the source star. We also discuss the event
The lens equation for the point mass len
s of caustic crossing. Such analytic studies of caustic
the macro lens model issing events should complement ray-tracing simula臨界曲線の
2
θ
θ
1
E θ1
s presented in [1] and [26] for which repeating simβ1 =
− 2 ,
µr
θ
サイズは
ions with many diﬀerent model parameters may be
2putationally expensive. Our approach more resemθE
θ2
θ2
− 2 .
2 =
θE βよりもthat in [27], which appeared when this work wasµtθ
ost completed.
Note that (β1 , ずっと大きいβ2 ) is the position of the shis paper is organized as follows. We present an anθ2 ) is the position of the image. The she
ic lens model which sets the theoretical backgroundaligned with x-axis. The inverse magnificection II. We then discuss what kind of constraints
! −1
2
2
⃗
can place from observed caustic crossing events in∂βµr + θ Ecos(2φ)/θ2
−θE
sin
=
−1
2
2
2
ion III. We apply our results to MACS J1149 LS1−θsin(2φ)/θ
µ
−
θ
⃗
t
∂θ
E
Ec
焦線は非常にderive constraints on lens and source properties ofparticular microlensing event in Section IV. We
The magnificationis
細長くなるがuss event rates and derive expected event rates for−1−1
CS J1149 LS1 as well as for general cases in Secµ−1 = (µt µr )囲まれる− (µ−1−µt ) cos(2φ)
r
V. In Section VI, we discuss constraints on compact
k matter in presence of ICL. Finally we summarize our
面積は ≈ θE
lts in Section VII. Throughout the paper we adopt
B. Critical curve and caussmological model with the matter density Ωm = 0.3,
mological constant ΩΛ = 0.7, and the Hubble constant
The critical curve can be derived from µ= 70 km s−1 Mpc−1 .
−1=0.001, μr−1=0.401) (μt−1=−0.001,ically,−1=0.399)(μμtr
G. 1: Critical curves (upper panels) and caustics (lower panels) of a point mass lens in the high magnification region. Left:ositive parity case with µ= 0.001 and µ= 0.401. Right: Negative parity case with µ=!
−0.001"and
2 µ = 0.399.
−1
t

−1
r

−1
t

−1
r

全増光率

正パリティでの光度曲線 (焦線2回通過)(μt−1=0.001, μr−1=0.401)

ソースの位置全増光率

負パリティでの光度曲線 (焦線4回通過)(μt−1=−0.001, μr−1=0.399)

ソースの位置11magnified near the center.
he behavior of the total magnification near the causs important for estimating the possible maximum
nification. The total magnification near the causs known to behave as µ ∝ ∆β −1/2 , where ∆β is thence between
the source and the caustic in the source
焦線近傍での全増光率は
e. We find that the magnifications near the caustics
rudely approximated
距離 Δβ →as0 で増大
!
"1/2
θE
µ(∆β) ≈ µt µr √
,
(25)
µt ∆β

漸近的振る舞い増光率•

h is reasonable given that the width of the caustic is√unk” by a孤立した点質量レンズに比factor of µt (equation 13).
quation (25) suggests that the magnification becomes
3/4
べ増光率は
μ
1 だけwhich ist toμther ≫caustic,r as the source approaches
iversal property of lensing near the caustic (see e.g.,
大きい (銀河団ポテンシャルと39]). However, the magnification saturates when the
点質量レンズ両方の増光の重ね合わせ)nce to thecaustic becomes comparable to the size ofource in the source plane, βR (e.g., [25]). From thisition, we can estimate the maximum magnification•

magnification factorµobs , which is derive
tudes measured at t
the lensed source isbecause the true ma
焦線event(caustics)
crossingis lardetection limit of mmust be smaller tha
Δβ
to caustic crossing,condition, we can reto∝Δβ−1/2

This means that, wh
the larger star simpl
ness, the microlensi
for the smaller star.
ソース
Δβ
位置
B.

Mac

t

to

which is reasonable given that the width of the caustic is√“shrunk” by a factor of µt (equation 13).
Equation (25) suggests that the magnification becomeslarger as the source approaches to the caustic, which isa universal property of lensing near the caustic (see e.g.,[38, 39]).
However, the magnification saturates when the
ソースとなる星は有限のdistance to the caustic becomes comparable to the size of
半径Rを持つthe sourcein the source plane, βR (e.g., [25]). From thiscondition, we can estimate the maximum magnification
as → 最大増光率が存在
!
"1/2
θE
µmax ≈ µ(∆β = R) ≈ µt µr √
.
(26)
µt R

√

有限ソースサイズ効果
増光率

•

III.

小さい星半径Rほど
EXPECTED PROPERTIES OF THE LENSAND SOURCE
大きい最大増光率 μmax
A.

Dependence on the source star

We discuss how the peak magnification scales with theradius R and luminosity L of a background star. Assuming the black body with the temperature T , they areThis means that, whi
the larger star simply
ness, the microlensin
for the smaller star.

R=0
B.

Macr

R≠0 prese
The analysis
form macro model mtice, however, the madepends on the imag
ical curve of the macµt quickly increases a
ソース
icalΔβ≈R
curve (see, e.g.,位置that we denotethe dcritical curve as θh , w
parametrize the depe

depends on the image p
AND SOURCE
we dical curve of thatthe macro
criticalascutµt quickly
We discuss how the peak magnification scales with
the increases
A. R Dependence
on theLsourcestarical Ascurve (see,e.g., [3parametr
radiusand luminosityof a backgroundstar.
that arewe denote the distsuming the black body with the temperature T , they
critical curve as θh , weWe
discuss
how
the
peak
magnification
scaleswiththerelatedas
大きい半径を持つ星は最大増光率
μがmax
parametrize
the depend
radius R and luminosity L of!a backgroundstar.
As"2 ! to"beAssuming
thetemperature
4 T = 12000 K (see [1]),suming the black body with
L the temperatureR
T T , they are
小さいが、そのような星はもともと明るい
the absolute=V -band magnitude. of the star (27)before therelated asLRTµt (θhµ) h=⊙⊙⊙ L: 光度wheremagnificationiscomputedusing
equation (27) as!
"2 ! "4
L
R
T
lens
mode
✓
◆
R:
半径
=
.
(27)
In practice Lthe spectralenergydistribution
(SED)
of
a
R
R⊙
T⊙
⊙
where µh is(49)aOnconstant
f
other
T:
温度
M
⇡
2.2
5
log
,
star does not strictly follow
star the black body, but this relens model asthe
well
as th
Ra
critica
In practicethespectralenergydistribution(SED)oflation still holds approximately. Using this relation,
we other hand, µOn
other
半径の大きい(もともとの光度が大きい)星
Therestarfind
doesthat
not strictly
follow
the
black
body,
but
this
rethe observed
maximum
fluxof theTstar
scales
where
we
used
M
⇡
4.8
in
V
-band,
=
5777
K,
and
the
criticalcurve.
L
lation still holds approximately. Using this relation, we
tween
β
h
as のほうが観測される最大明るさは大きい
There
is
also
a
wellincluded
thebolometriccorrection.
Therefore,takingacfind that the observed maximum flux of the star scales
sourcepla
tween
βh (thecount of the cross-filter
K-correctionin [1],
the angular−1/2
3/2 4derived
ascurve
fmax ∝ µmax L ∝ R
L ∝ R T . source(28)plane)ical
and
θh (t
minimum apparent
magnitude
of
the
star
magnified
by
−1/2
3/2 4
ical curve in the image p
fmax
∝
µ
L
∝
R
L
∝
R
(28)
max
microlensing
at the peak isT .

増光された星の観測可能性••• 具体的に Icarus の場合
✓

◆

✓

◆
200 R
M
mpeak ⇡ 25.5 3.75 log
0.625 log
(50)
.
R
M
ソース星の半径点質量レンズ質量The observation indicates that the peak magnitude ispointmass lenses
the same mass
Mother. As hasthereforesatisfyhave
this condition.
On theabove,
component
has the surface
densi
the theotherICL
condition
for non-saturation(equatioΣICLhave≈ 7 M⊙ pc−2 (which corresponds to the masstion of fICL = ΣICL /Σtot ≈ 0.0035), and therefore
7
isfy this condition. OnMthe
other
hand,
. 5.1
⇥ 10
M .from thecondition for non-saturation (equation 40) we can
For MACS
LS1, asthe source crossing tim
constraints
on theJ1149
lens mass
Icarusの場合
41) istsrc ≈ tion
2R/v
M ! 5.1◆×⇣107 M⊙ .
✓
⌘ 1
200 R
v
tsrc ⇡ 7.6
days.
1
For MACS J1149 LS1,
crossing
time (
R the source
500 kmstion 41) is ソース星の半径 相対速度
Similarly, the time scale between caustic crossin
!
"#
$−1
R
v
⌘ 1
tsrc ≈ 0.019 ✓ M ◆1/2 ⇣ −1v
days.
500 km stEin ⇡ 3.5R⊙
yr.
1M
500 km s
Similarly, thetime scale between caustic crossings
時間
J1149 LS1, the source crosstEin ≈ (θE/√μt)/v In the case of!MACS"1/2 #where the light$−1 curve iswhich is the timescalev
M
yr.
tEin ≈ 3.5−1
M⊙
500 km s

明るさ

光度曲線の時間スケール•

点質量レンズ質量 相対速度

In the case of MACS J1149 LS1, the source crossing
appears to be smaller than ∼ 10 days [1]. The cond
tsrc ! 10 days becomes
!
"#
$−1
R
v
! 530

MO, Diego, Kaiser, Kelly & Broadhurst, arXiv:1710.00148

レンズとソースへの制限
8(shaded: excluded)• Icarusの場合の制限• レンズ質量はICLの星の質量 (~1 Msun)

レンズ質量

と無矛盾

• 最大増光率はソース星の半径

FIG. 2: Constraints on the source radius (R) and lens mass(M ) for MACS J1149 LS1. Shaded regions show excluded

R ≈ 180 Rsun およびM ≈ 0.3 Msun の場合
μpeak ≈ 4300

toward the critical curve. This is becausethe
EinDiego, ..,MO+,
arXiv:1706.10281
radius of the point mass lens depends on µt as√
サチュレーション
Einstein radiiµt , and hence
for very large µt the (Saturation)
diﬀerent point mass lenses overlap, even when thewhich rber density of point mass lenses is small. As shown
ay-tracing simulations in [26], beyond this “satura” point thesourcebreaks into many micro-images,≈√μtθ E
as a result it loses its sensitivity to the source posiwith respect to the macro model caustic. Therefore,
In pracmacro model低質量密度magnification
in
fact
does
not
divergeΣ
高質量密度 Σditions,
redicted by equation (31), but saturates at a finite
Fromt
点質量レンズの数密度が十分大きくなると•e.
maximuo estimate
where the saturation happens, [26] considアインシュタイン半径が重なってくる
the optical depth τ defined by→ 増光率がサチるΣ √2τ=π ( µt θE Dol ) ,Mτ≳1 → (33)
サチる

which i焦線通過: 定性的理解• 臨界曲線から• 中心部では平均

μ不十分
増光率

遠いと不十分な
増光率

臨界曲線

Icarus

観測可能

μ不十分

サチュレーション

増光率がサチる• 焦線通過は「正しい」範囲でのみ観測される点質量レンズあり

完全になめらか
臨界曲線
からの距離

sity
The
d so
)dL
the
L⊙ ,
um-

B. Expected
small rectangular region
shows the rate
rough mass fraction andthe mass range of ICL stars. Contours show the constant evenratein thisFrom
to outer
contours,
we showFrom
the plane.
analysisin−1inner
Section
II,
we
know
that
the
−2
−3
−4
−5
contours for dN/dt = 10 , 10 , 10 , 10 , and 10 .

イベントレート
typical length scale of the caustic along β direction is√≈ 2(µ /µ )θ . Therefore the expected event rate is
焦線通過の期待されるイベントレート
•
(
√
1

t

r

E

θh,maxB. Expected rateΣ
µt 2
dN
= 2
dθh nstar warc µt µr 2
Dol θE u,dt
M µr
θh,min$"II, we#know% typFrom the (analysis in Section
that
the
#
"
2
2
µt,max焦線の長さµh dµR⊙ the β1Rdirection# ical length scale of thet⊙causticalongisn0− × 相対速度√= 2
L⊙
2≈ 2( µt /µr )θµEt,min. Therefore
eventµt the expected
R1
R2 rate is
FIG. 4L2√点質量レンズ臨界曲線
lens ma( θh,max√mΣ
のpeak<mµlim
t 2 アーク
µ
dN
Σ
t 2
2
D
θ
u,
(63)
×w
E
arc
の数密度
ol
からの距離
(60)
= 2
µt µr 2Dol θE u,星の数密度
Mdθh nµstar
r warcの幅
dt
M(ソース平面)µr
θh,min)( θh,min to be 0.2 arcsec in the√following calwhere warc (assumed
)
µt 2
Σ
Amon
)
is the width
the
giant
dθhof
nstar
warc
µt µrarc 2along theDol θcriticaling culations)+2
E u)
and (4M theµr upper limit0µ
curve,
andthesaturation
conditions
give
t,max
ing
$"
%
fined i
#
#
"
(
2
2
µ
µ
.
The
factorµµconverts
thenumberdensityoft,maxサチった中心領域からの寄与
vert
t,max
R⊙
R⊙
µhtdµrtdetermn−=2
the point mass lens in 2the image
plane, Σ/M , to the cor0
µt
R1
R2
to
µ
t,min
responding number density in the source plane. The pref√MO, Diego, Kaiser, Kelly & Broadhurst, arXiv:1710.00148

Icarus領域のイベントレート
9点質量レンズの質量割合(shaded: excluded)

多くの点質量レンズ
強いサチュレーション

少ない点質量レンズ
弱いサチュレーション• ICLの星で観測
レンズ質量FIG.最大増光率小さい
3: Constraints in the M -fp planefor MACS J1149 LS1,
平均自由行程大きい
where M is the lens mass and fp is the mass fraction of theされたレートを説明可能MO, Diego, Kaiser, Kelly & Broadhurst, arXiv:1710.00148

レートを含めた制限
10(shaded: excluded)• イベントレートからの制限を追加• ICLの星 (~1 Msun) はレンズ質量

依然として無矛盾

ソース星の半径
FIG. 4: Similar to Figure 2, but additional constraint on thelens mass range from the event rate (see Figure 3) is included.

コンパクトダークマターへの制限
増光率

サチュレーション

低密度
コンパクトDM→ 高い最大増光率
高密度
コンパクトDM→ 低い最大増光率

臨界曲線
からの距離

• ICLの存在下でコンパクトダークマターを制限可MO, Diego, Kaiser, Kelly & Broadhurst, arXiv:1710.00148

コンパクトダークマターの質量割合

コンパクトダークマターへの制限•

the robust interpretation
密度が高すぎるclue may be obtained b
curves before and afterと強くサチってin order to obtain robu
matter from observation
最大増光率が
ray-tracing simulations t
compact dark matter, a
小さすぎ観測を
tracing simulations are hkind light curves such co
説明不可
VII.

コンパクトダークマターの質量FIG. 7: Constraints on the mass (M ) and abundance (fp ) ofcompact dark matter. Shaded regions show excluded regions

SUMMAR

In this paper, we havemodel that consists of aconvergence and shear fi
ing properties of a poinmagnification regions duMO, Diego, Kaiser, Kelly & Broadhurst, arXiv:1710.00148

コンパクトダークマターの質量割合

コンパクトダークマターへの制限•

the robust interpretation
密度が高すぎるclue may be obtained b
curves before and afterと強くサチってin order to obtain robu
matter from observation
最大増光率が
ray-tracing simulations t
compact dark matter, a
小さすぎ観測を
tracing simulations are hkind light curves such co
説明不可
VII.

詳細な光度曲線解析？
コンパクトダークマターの質量FIG. 7: Constraints on the mass (M ) and abundance (fp ) ofcompact dark matter. Shaded regions show excluded regions

SUMMAR

In this paper, we havemodel that consists of aconvergence and shear fi
ing properties of a poinmagnification regions duまとめ• 銀河団の高増光率領域において全く新しいタイプの変動天体を発見した• 巨大アーク内の単独の星が銀河団内のコンパ
クト天体により非常に増光されたものと解釈できる (μpeak ≳ 4000 for Icarus)• IcarusイベントはICLの星によって引き起こされたという解釈と無矛盾• 解釈は複雑だがDM研究の多大なポテンシャル• さらなる理論的/観測的研究が待たれる