in collaboration with

Re’em Sari (Hebrew/Caltech), Elena Rossi (Hebrew) , P. Laguna (Georgia Tech),

E. S. Phinney (Caltech), P. Meszaros (Penn State)

•! Stars

–!Fallback debris & X-ray/UV Flares

–!Tidal compression & prompt X-ray

•! Binaries

–!Hypervelocity Stars

–!New Approximation Formulae

Tidal disruption of stars/binaries by MBH

m2~!

!

MBH

= Msun

!

"a =2GM

BH

R3

# = 2 $1010m/s

2

Acceleration on Earth 2m/s10~

Difference in acceleration

sunBHMM6

10=

!

"a =2GM

BH

RBH

3# ~ 0.02m/s2

!

Gm

r"2

~GM

R3r" # R

tidal=

M

m

$

% &

'

( )

1/ 3

r"

star BH

!r

m

:size

:mass

M:mass

!

R

Self gravity Tidal force

!

Rhorizon

"M

!

Rtidal

"M1/ 3

BH

TAIDAL RADIUS

Tidal force dominant

self gravity

internal pressure

Snapshots of a disrupted star

Kobayashi, Laguna, Phinney & Meszaros et al. 2004; Rantsiou, Kobayashi, Laguna &Rasio 2008

Artist’s impression (NASA/ESA)

!

E > 0

!

E < 0

fly away

Fallback

disruption

!

L"dm

dt=dm

dE

dE

da

da

dt"dE

da

da

dt

!

binary : E = "GM

BH

2a , t # a3 / 2

Rees 1988, Phinney 1989

!

" t#5 / 3

mass accretion rate of fallback debris

Each debris with E < 0 forms binary with MBH

A tool for probing Quiescent Massive BHs

•! Currently a dozen candidates of tidal flares

–! ROSAT, XMM-Newton Slew Survey

–! GALEX Deep Imaging UV Survey

AGNs: Loud MBHs

X-ray Flare

ROSAT: all-sky survey

-- RX J1242.6-1119A

Gezari et al. 2006

GALEX Deep Imaging Survey

No evidence of Seyfert nucleus

from optical spectroscopy and X-ray imaging

UV flare

no sources

!

L ~ t"5 / 3

Upcoming Surveys

•! Optical “All-Sky” Surveys

–!PannSTARRs

–!Palomar Transient Factory

–!LSST

•! X-ray All-Sky Monitor in the Next Decade

–!EXIST

•! Gravitational Wave Antenna in near future –!LISA

hundreds events yr^-1

Strubbe&Quataert2009

Tidal compression

and

Early X-ray Flash

Stretch: radial direction Compression: transverse directions

Arp 240: NGC 5257, 5258

!

"(! x ) ="(

! R +! r )

# "(! R ) + ri $xi

"[ ]x= R

+1

2rirj $xi

$x j"[ ]

x= R+ ....

CM

R

!

x!

r!

BH

star

Rr <<

!

d2xi

dt2

= "#xi$(! x )

% " #xi$[ ]

x= R" rj #xi

#x j$[ ]

x= R

Acceleration at CM Tidal acceleration

Inducing motion relative to CM

!

d2ri

dt2

= " #xi#x j$[ ]x=R

rj

Equation of motion of a star element in the center-of-mass frame

!

"(! x ) = #

GMBH

xDiagonalize the symmetric tensor

!

"1

= +2GM

BH

R3

"2

= "3

= #GM

BH

R3

$

% &

' &

Eigenvalues

BH Gravity potential

Stretching

Brassart&Luminet 2008

Stretched toward BH

Compressed in two transverse directions

one of compression directions is always normal to orbital plan

!

ˆ e 1

=| R

2|

R

R1

R2

ˆ x + ˆ y "

# $

%

& '

ˆ e 2

=| R

1|

R(

R2

R1

ˆ x + ˆ y "

# $

%

& '

ˆ e 3

= ˆ z

Luminet & Marck 1985

!

"N

!

"S

Tidal force

Thermonuclear Detonation? --- still in debate

Shock Heating? ---- I will show at least this should happen

Flat and Hot

•! Hydrodynamic model of a Star –! 1dim Godunov method, 3dim SPH

–! Model the time dependent tidal field corresponding to a star in a parabolic orbit

–! Shock forms around compression point

–! Shock heats the star including “its surface”

–! X-ray emission expected

Kobayashi et al. 2004

!

D =Rperiapse /Rtidal = 0.1

Shock heating

At shock breakout

surface temperature is

comparable to at the center

Kobayashi et al. 1999, 2004; Brassart & Luminet 2008, 2009; Guillochon et al. 2009

time evolution of pressure distribution

time evolution of density distribution

10^6 Msun BH +solar-type star

(Polytrope n=3/2)

Godunov with exact Riemann solver

Due to relativistic precession effect,

Orbit winds up around the BH

Star compressed twice

X-ray obs could help GW detection

BH mass, spin, orbit periastron

Prompt X-ray Signal GW signal

3dim Relativistic SPH

!

D = Rp /Rtidal

!

D =1

!

0.2

!

0.1

!

M =106Msun,d = 20Mpc

Kobayashi et al. 2004

keV 1~~

ergs104~~ 482

!

!

!

! "

R

mGMTk

R

GME

p

B

theraml

Crossing time of a star through compression point ~ 10-100 sec

After compression, the star stretched

thermal energy --> kinetic energy

solar type star

How much energy coming out as radiation?

erg/s10~Lergs10~E~E 4243

thermal !""#

$%%&

'

(R

D

D

Considering random walk, diffusion scale is

Energy of escaping photons

!

D ~ N1/2! ~ c "t

R#

$

%

& '

(

) *

1/ 2

, D /R# ~ 10+5

How about emission during stretch/disruption phase? Optical depth drops

Ionized hydrogen: energy tapped from recombination (Kasen&Ramirez-Ruiz2009)

10

210~

4~

!

!

Rm

M

p

T

"

#$

Sun mean free path ~ cm

photon diffusion from the core: 10^4-5 yrs

Soderberg et al. 2009

X-ray transients Optical transients

Rau et al. 2009

x-ray prompt emission due to tidal compression

flares due to fallback to BH

Meeting with a monster BH at the Galactic Center

the end of road for stars?

Stars with a velocity > escape velocity

Found in the halo 50-100kpc

B-stars (blue stars: obs strategy)

30kpc

8kpc

Brown et al. 2005, 2009, Hirsch et al. 2005

just a beginning for some stars…..

Binary disruption by massive BH Hills 1988

SMBH

high v

Other scenarios: star with intermediate mass BHs (Hansen&Milosavljevic 2003;

Yu&Tremaine2003; Levin2006), interaction with stellar BHs in the GC (Yu&Tremaine2003; Miralda-Escude&Gould2000;O’Leary&Loeb 2007)

•! Almost all HVSs: positive radial velocities

•! Consistent with picture –! they coming from the Galactic center

–! GC is full of B-type stars

•! Travel time from the GC: ~150Myr –! Lifetime of 3 solar mass star ~ 350Myr

–! Bounded population

Radial velocities: 759 stars

HVSs

Brown et al. 2009

Taking the Galactic potential into account

over 1000 km/s from the bulge

HVSs in broader context

•! The properties linked to –! Massive BH ( or MBH binary)

–! Stellar environment of the Galactic center

•! In-fall history of stars, Stars orbiting the BH

•! Probe of the Galactic dark matter potential

•! The nature of ejection mechanism

e.g. Sesana et al. 2007; Kenyon et al. 2008; Perets 2009

!

{

!

"E ~ vbinaryvCM(Rtidal)

!

v ~ "E ~ M /m( )1/ 6vbinary

BH

!

Rtidal

!

vbinary ~ Gm /a

!

vCM

= GM /R

t

E

!

E ~ 0binary’s center of mass

binary rotation

!

< 400km/s m

msun

"

# $

%

& '

1/ 2

a

rsun

"

# $

%

& '

(1/ 2

•! Gravitational potential energy –! The displacement of order a in the position of each

component around tidal radius.

•! Work –! Energy of each component is changing only due to

self-gravity force which acts over length

BH0

2vv~/~

tRGMaE!

2/ aGm

tR~

BH0

2vv~/~ aGmRE

t!

!

"E

•! Previous investigations

–! Full three-body simulations

–! Only a limited set of parameters (e.g. binary mass ratio)

•! We have developed new approximation formulae

–! Binary separation << distance to BH

–! Since , is required

–! Faster (smaller number of eqs, larger time-step for integrations)

–! Parameter dependences come up analytically

!

Rt

= M /m( )1/ 3

a

!

(M /m)1/ 3

>>1

Three body problem

!

r1

!

r2

!

m1

!

m2

!

M

!

m = m1+ m

2

!

R

!

a << R

Linearizing BH gravity terms around the CM of binary

Equation for the distance between two

!

! r =! r 2"! r 1

!

d2! r

dt2

=GM

R3"! r +

3(! R ! r )

R2

! R

#

$ % %

&

' ( ( +

Gm

r3

! r

Tidal Force Self-Gravity

!

" #xi#x j$[ ]x=R

rj

f: Angle from the point of the closest approach

!

length in unit of (m/M)1/3rp

time in unit of rp

3 /GM( )1/ 2

CM in a parabolic orbit

!

d2! r

dt2

=rp

R

"

# $

%

& '

3

(! r + 3( ˆ R

! r ) ˆ R ( ) +

! r

r3

!

ˆ R = (cos f ,sin f ,0), rp /R = (1+ cos f ) /2

df /dt = 2(1+ cos f )2/4

equivalent to Hill equations for parabolic orbit rather than circular problem e.g. Sun-Earth- satellite

!

{

•! If self-gravity term is neglected –! this is valid when binary crosses tidal radius

•! we have analytic solutions –! a set of 3 linear differential eqs of 2nd order

–! a liner combination of 6 independent solutions

–! used to understand the behavior of binary inside tidal radius

!

! r /r

3

•! Comparison: 3body and our formula

secondary orbit Energy of the secondary

difference: 3-body and the approx estimates: ~0.1%

3body

approx

!

E1

= "E2

=Gm

1m

2

a

M

m

#

$ %

&

' (

1/ 3

F(D,))

Penetration factor: D=(closest approach to BH)/(tidal radius)

Binary phase:

!

"

!

E(" + # ) = $E(")

Final energy of a binary star as a function of initial binary phase

!

D = 0!

D =10"3,10

"2,3#10

"2

!

energy in unit of (Gm1m2 /a)(M /m)1/ 3Sari,SK & Rossi 2010

Contrary to the previous claims

Upon binary disruption, the lighter star does not remain preferentially bound to the BH.

In fact, it is ejected in exactly 50% of the cases. Nonetheless, the lighter

stars have higher ejection velocities, since the energy distribution is independent of mass.

MBH

prograde

retrogarde

even deep penetration cases

20% binaries not disrupted

Sari,SK & Rossi 2009

disrupted

tightened

secondary star position in the primary rest frame

prograde

retrograde

~27

!

energy in unit of (Gm1m2 /a)(M /m)1/ 3

Sari,SK & Rossi 2009

averaged energy

over binary phase

max energy

for different binary phases

•! ejection velocity

!

v1

= 2E1/m

1

!

velocity averaged over phase in unit of 2Gm2 /a M /m( )1/ 6

Sari,SK & Rossi 2009

•! Our analytic approach allows us to

rescale our results in terms of a given

minimal distance over the whole

evolution, instead of a given initial

separation.

Summary

•! Stellar Pancakes –! Shock formation due to tidal compression by a MBH

–! Shock breakout X-ray emission

–! upcoming All Sky surveys •! optical: tidal flares with long timescales ~ years

•! X-ray and GWs: burst events ~ 100 sec

•! Hypervelocity Stars –! leading model: tidal break of a binary by a MBH

–! new approximation formulae

•! equivalent of Hill equations for parabolic rather than circular problem

•! mass, binary separation dependences come up analytically

•! analytic solutions for binary evolution deep inside tidal radius

–! ejection chance is 50-50 for disrupted binary members

–! even in deep penetration cases, 20% binaries not disrupted.

–! High disruption chance, high ejection energy/velocity are achieved around D=0.1-1

Two kinds of objects related to the tidal fields of MBHs

•! The orbit of CM

–!Relativistic precession effect

•! Tidal gravitational field

zR

L

R

GMztg BH

!!"

#$$%

&+'=

2

2

3

31),(

Parabolic:

1

21

!

""

#

$

%%

&

'!=

p

g

gpR

RRRL

Star size much smaller than spacetime curvature radius

Newtonian description of its internal motion (Euler eqs)

)(tRR =

prograde

retrograde

Final energy contour plots

!

energy in unit of (Gm1m2 /a)(M /m)1/ 3

Sari,SK & Rossi 2009

Untargeted Transient and Variable Surveys: Optical