Mészáros gw05

GRB and BHas

Gravitational Wave(and EM)

SourcesPeter Mészáros

Pennsylvania State University

Mészáros gw05

GRB Sky & Temporal Distrib.• Cosmological distrib.

(isotr.) ~3500 bursts• Out to z t 4.5 (20?)• ~ 1/day @ z d few• ~ 2/3 “long” (tg >2s)→ massive coll/SN?~50 afterglows well-id’d & localized

in g,X,O,R, measured redshift;massive ø progenitor ~confirmed

• ~ 1/3 “short” (tg <2s)→ NS mergers?

5 afterglows so far, host galaxies at 0.2 ≤z≤0.7, 4 Elliptical, 1 Irreg.

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GRB-GW: Progenitor Rates & Min. Distances for 1 event/year

23-1102710-1000630Collapsar

62-490950.1-5014BH-He

230-49004300.0001-10.15BH-WD

62-23002800.001-500.55BH-NS b

62-23001700.001-502.6BH-NS a

53-11002200.01-80.1.2DNS

MpcMpcMyr-1gal-1Myr-1gal-1Dist-rangeDist (avg)Rate-rgeRate (avg)Progenitor

(Data from Fryer etal, 99, ApJ 526,152; Belczynski etal, 02, ApJ 571,394)

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LIGO•≠Hanford (WA) site,

+ Livingstone (LA) • 4 km Michelson interf.,vacuum laser refl.

• Sci. runs started in 2002

VIRGO→• Italian/French: @ Cascina, Pisa →• 2x3 km arms laser interf.• Completed June 03, comissioning

• Science goals: test GR +• Compact bin. inspiral (dns,dbh,nsbh)• GRB, core-coll. SN, NS r-mode osc.• Stochastic GW backgr (inflation)• Also : Geo-600, TAMA

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Simple astrophysical GRB GW model:

either bin.merger or collapsar: fi as if blobs orbiting

(fast rot. fi instab. fi blobs fi merge ;

or: double NS, NS/BH: blobs fi merge )

(Shiho Kobayashi & PM ‘02)

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1: In-spiral phase

• Inspiral of m1, m2 (binaries or blobs): hc(f) = f |ĥ (f)| : characteristic strain<r2>= 4 ∫ | ĥ | 2 /Sh ) df =(2/5p2d2) ! df (1/ f2 Sh)(dE/df)dE/df = [(pG)2/3 /3] M 5/3 f -1/3 : energy sp. [Flanagan, Hughes 99]

M = (m1 m2)3/5/(m1 +m2 )1/5 : chirp mass

• → hc(f) ~ (1/pd)[(G/10c3)(dE/df)]1/2

~1.4 10-21(d/10Mpc)-1(M/M )5/6(f/100Hz)-1/6

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Merger• binary (or coll. blob) in-spiral ends (DNS/BH-WD-He) at

fi ~ 103 (M/2.8 M ) -1Hz / 0.1(M/ M )1/2 (l/109cm)-3/2 Hz• Merger ends (quasi-normal ring l=m=2 starts) at

fq ~ F(a) c3/2p GM ~ 32 F(a) (M/ M )-1 kHz ; [ F(a)=1-0.63(1-a)3/10 ]

• En. Radiated: Em= em (4m/M)2 Mc2 ; [em ~ 5%, m=m1m2/M]• dE/df ~ Em /(fq –fi ) ~ Em /fq (asume simple flat spectrum)• hc (f) ~ (1/pd)[(G/10 c3)(dE/df)]1/2

~ 2 .7 .10-22 F(a) -1/2 (em /0.05)1/2(4m/M)(M/ M )(d/10Mpc)-1

(e.g. Lai & Wiseman 96; Khanna etal 99; Flanagan & Hughes 98)

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Bar / Dynamical Instabilities• Bar mass m, length 2r, around BH mass m’,

rot. freq. w =(Gm’/r3)1/2

• Disk: dynamical instab. → blob, mass m ~a Maround BH mass ~3-10 M

• Both → similar expression ,h = (32/45)1/2 (G/c4)(mr2 w2/d) hc ~ N1/2 h [N : # of cycles of approx. coherence ~10]

~2.10-21 (N/10)1/2 (mm’/ M 2)(d/10Mpc)-1 (r/106 cm)-1

(e.g. Fryer, Holz & Hughes 02)

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Ring-down• Deformed BH → damped oscillations,

slowest mode: l=m=2 (also pref. excited)• Spectrum peaks at fq ~32 F(a)(M/)-1 M kHz,

width Df ~ t-1 ~p fq /Q(a) ; [ Q(a)=2(1-a) -9/20 ]

• dE/df ~(Er f2 /4 p4 fq2 t3 )..[(f-fq)2 + (2pt)-2]-2 +[(f+fq)2 + (2pt)-2]-2

(where Er= er (4 m/M)2 Mc2 , assumed er =0.01 rad. en.)

• hc~2. 10-21 (er /0.01)2(Q/14F)1/2(m/ M )(d/10Mpc)-1

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GRB Progenitor GW Signals: DNS

f [Hz]

hc

100

101

102

103

104

105

10−24

10−23

10−22

10−21

10−20

DNS

(a)

(b)

Solid: inspiral; Dot-dash: merger; circle (bar inst); spike: ring-down); shaded region: rate/distance uncertaintyKobayashi & Mészáros 02, ApJ 589, 861

Double neutron starCharact. Strain hcD (avg) =220 Mpc, m1=m2=1.4 Ma=0.98, em=0.05, m=m’=2.8 M , N=10, er=0.01

Dashed: LIGO II sensitivity

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GRB Progenitor GW Signals: BHNS

f [Hz]

h c

100

101

102

103

104

105

10−24

10−23

10−22

10−21

10−20

BH/NS

(b)Black hole-neutron starthin: d=170Mpc, m1=3.0 M , m2=1.4 M ,m=0.5 M , m’=4 Mthick: d=280Mpc, m1=12 M , m2=1.4 Mm=0.5 M , m’=13 M ;

Both: a=0.98, em=0.05,N=10, er =0.01

•Solid: inspiral; Dot-dash: merger; circle (bar inst); spike ring-down); shaded region: rate/dist uncertaintyDashed: LIGO II noise [f Sh(f)]1/2

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GRB Progenitor GW Signals: CollapsarCollapsar w. core breakup, bar inst.(optimistic numbers!)d=270 Mpc, m1=m2=1 M , a=0.98,em =0.05, merge at r=107 cm; m=1 M , m’= 3 M , N=10, er =0.01

Dashed: LIGO II noise [f Sh(f)]1/2

(b)

Solid: inspiral; dot-dash: merger; circle :bar inst; spike: ring-down); shaded : rate/dist uncertainty

f [Hz]

hc

100

101

102

103

104

105

10−24

10−23

10−22

10−21

Collapsar

Kobayashi & Mészáros 02, ApJ 589, 861

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Detectability :upper limits, in one year LIGO II

• BH-NS, NS-NS: wave templates → matched filtering;

S/N : r = [ 4 ∫ ĥ(f)|2 /Sh(f) df ]1/2 ≥ 5 ( Sh (f): det. noise )

• rDNS,insp ~ 7.5 (1.5,30) (M/1.2 M )5/6 (R/1.2 Myr-1 g-1)1/3

• rBHNS,insp (a) ~ 13 (0.9,35) (M/1.8 M )5/6 (R/2.6 Myr-1 g-1)1/3

• Collapsars: No templates → cross corr of 2 det. output[ Finn et al, 99 ; Finn, Krishna & Sutton, astro-ph/0304228]

Xon ~! df ∫ df’ dT(f-f’) ŝ1*(f) ŝ2 (f’) Ĝ(f’) soff = avg [(n1,n2)2 ]1/2 ~ C [(T/4) ! df /S2 (|f|) ]1/2

S/N : r= Xon / soff t 5 • rColl,merg ~ 3 (em/0.05) (F[a]]/0.8) (T/10 s)-1/2

. (m /0.5 M )2 (R/630 Myr-1 gal-1)2/3

[ Kobayashi & Mészáros 02 ApJ 589, 861 ]

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Detectability :Collapsars: upper limits, in one year LIGO II:

• No templates (e.g. merger, ring-down):→ use cross correlation of 2 det. output

[ Finn et al, 99 ; Finn, Krishna & Sutton, astro-ph/0304228]

• si (t)= hi(t + ni(t); ni(t) =detector noise; [spatial coincidence : through arrival time correction];

signal weighted cross correlation : [G: filter function] Xon ~∫ df ∫ df’ dT(f-f’) ŝ1*(f) ŝ2 (f’) Ĝ(f’)

noise fluctuation cross correlation : [ T= gw-g lag ] :soff = avg [(n1,n2)2 ]1/2 ~ C [(T/4) ! df /S2 (|f|) ]1/2

S/N : r= Xon / soff t 5

• rColl,merg ~ 3 (em/0.05) (F[a]]/0.8) (T/10 s)-1/2

. (m /0.5 M )2 (R/630 Myr-1 gal-1)2/3

[ Kobayashi & Mészáros 03, ApJ in press (astro-ph/0210211 ]

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Suspended collapsarGRB

• Specific GRB model: collapsar → BH + torus, when WH >WT →“suspended” accretion

• Blue: char. diml’ss strain hchar B1/2/51/2 , for MBH=4-14 M , h=WT/WH~0.1, B~10%, D=100 Mpc (1/yr)

HΩ

ΩT

0 200 400 600 800 1000 120010

−23

10−22

10−21

10−20

MH=14M

o

η=0.1

frequency [Hz]

dim

en

sio

nle

ss s

tra

in a

mp

litu

de

Adv LIGO

Initial LIGO

D=100Mpc

Initial VIRGO

Cryog VIRGO

Van Putten, Levinson etal 03, gr-qc/0308016 ;( also 03, ApJ 584, 937)

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GW PolarizationKobayashi & Mészáros 03, ApJL 585, L89

• hTT ∂ [ ““ Y22 ]TT (transv. traceless comp.)

h+ ∂ (1+cos2 a), hx ∂ 2 cosa , hi = Re Ai exp[-iwt] ,

where for l=m=2 mode A+ ∂(1+cos2 q), Ax ∂ 2i cos q(a: angle resp. ang. mom; q: viewing angle )

Pol. Tensor rab = <Aa Ab* >/<|A+|2 +|Ax|2> ==(1/2)( 1+x3 x1-ix2 )

( x1+ix2 1- x3 )x1 =0, x2 =f(q) → circular polarization, x3 = 2(1-cosq)2 (1+cos q)2 /[(1-cos q)4 +(1+cosq)4 ] ª P → lin. polariz.P~ 10-2 (q /30 o)4→ degree of lin. polarization of GW (while Lg µ q -2 → g-ray lum. of long GRB (collapsar?))

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Polarization Detectability• Need 2 detectors with non-paralell arms• At least S/N r ¥ P-1 to detect linear pol. deg. P ;

(from num. sim. → need r =10 P-1 )• Collapsar: r ~ 16 (d/100 Mpc)-1

→ optimal orientation, P=1% if dmax <3.5 Mpc• But, 103 grb/yr at <3 Gpc →<dmin >~300 Mpc• LIGO II sensit’y @ f0~150Hz :

[f0 S(f0 )]1/2 ~ 3.10-23 Hz-1 , and dmax ∂ S0-1/2 ;

→ if future detector with [f0 S(f0 )]1/2 ~ 3.10-25 Hz-1

→ may detect P~1% in 1 yearKobayashi & Mészáros 03, ApJL 585, L89

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Some potential GW-EM correlations in GRB

• DNS/BHNS: good GW source, but weaker (less collimated) GRB - expect “short” (<2 s) GRB, no (or weak) afterglow (?)

• Collapsar: weaker GW source, but strong and “long” (>2 s) GRB, with many EM afterglows observed

• GW for both may be detectable w. LIGO II ( Kobayashi & Mészáros, ApJ(a-ph/0210211)

• non-aligned jet obs. at G~qj-1 , and G∂t-1/2

→ afterglow peaks at time tp∂ q2 after GW → P ∂ tp2

• XRFs: may be misaligned jets, →preceded by GW, XR softness ∂ tp1/2 (Kobayashi & Meszaros 03 ApJL 585, L89)

• Collapsar: BH of ∫ ang. rot. rate “a” have ∫ polar accr. rates, hence ∫ polar infall turnaround times (GRB “explosion”), → predict ∫ delays between GW and GRB as function of stellar mass & BH rotation rate a (e.g. for M* = 40 M , tdel ~ 50, 60, 104s for a=0.95, 0.75, 0

(Fryer & Mészáros 03 ApJL, a-ph/0303334)

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On the tracks of the SMBH

(… do they really exist ?? )Direct black hole mass/size determinations:

• dynamic mass measures:- gas disk dynamics (HST, on AGN, ~ few pc)- stellar proper motions in gal. center, ~ lightyear- water maser (radio, NGC4258, ~ 0.4 lightyear)

• relativistic effects on spectral lines:- Doppler broadened (asym.) Fe K-α (X-ray, AGN)- Doppler broadened (asym.) H Ly-α (opt., AGN)

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Milky Way galactic centerstellar dynamics

In IR light (gets through dust); Genzel, Townes, Ghez et al,. ...

Mass density profile solution: fl 2,6. 106 M point-like mass neededplus ~ 4.106 M stellar cluster, all within ~ 0,4 pc radius

(Genzel et al, 2OO2)

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

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H2O maser radio lines

The water maser narrow radio emission lines in NGC 4258 (distance 6.5 Mpc) are outstanding for delineating the molecular gas disk velocity profile. (The conditions for maser action are only rarely fullfilled in AGN disks, but it is more frequent in galactic sources).

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H2O maser: NGC 2458

(Greenhill et al 1995)

• Radiation pressure of X-rays from the inner disk compress the outer disk, favoring molecule formation at T≤1000K (H2O, etc) and creating conditions favorable for maser action . The masers lie on an almost straight line arrangement, showing that the disk is warped (which makes the illumination by central X-rays possible). The water maser narrow radio lines are outstanding kinematical tracers. The resulting rotation curve implies the existence of a massive point source (~106 M ).

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Massive Black Holes (MBH): Star Trappers & Wreckers, Inc.

• In galactic nuclei (r < rc ~ 0.5 kpc) the stellar mass density n*m* can exceed the mass Mh=106 M of the central BH: Mh << n* m* rc

3 , for r < rc ,• but: BH sphere of dominance: (GMh/r)1/2 ≥ σ(r)

→ rh=GMh/σ2 = (Mh/n*m* rc3)rc

→ BH dynamically dominant for r ≤ rh

• Stellar visiting or infall rate into the region r ≤ rmin

º 10-4 M64/3 (n*/105 pc-3)(σ/100 km s-1)-1 (rmin/rt) yr-1

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Stellar disruption

• If the star’s self-gravity ≤ tidal(BH differential grav.) force:Gm*/R*

2 ≤ GMh [1/r2 -1/(r+R*)2] ~ (GMh/r2)(2R*/r)

→ Gravitational disruption,inside the tidal radius rt ,r ≤ rtª(2m*/Mh)1/3 R*º 5.1012 M6

1/3(r*/r )(m*/m )-1/3 ,

• Compared to the Schwarzschild radius, Rg=2GMh/c2=3.1011M6 cm,

rt/Rg ~24 (R*/R )(m*/m )-1/3M6-2/3

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Disruption and Swallowing• Different stars have tidal

radii rt comparable to Rg ,, the Schwarzschild radius of different mass MBHs

• E.g, a solar type star captured by a 108 M BH can be swallowed in one piece (no disrupt., rt <Rg)

• A 106 M BH can disrupt a solar type star, but:

• for a subsequent rapid swallowing one needsrp << rt →penetration factor

βp=rt/rp >>1• He stars (smaller radius)in

the same BH have rt ~ Rg , i.e. the disruption always leads to rapid swallowing

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Stellar wrecking

(Kobayashi, et al, ApJ in press, astroph-O4O4173)

Solar type stellar orbits, ↑ for penetration param βp = rt/rp = 1, 5, 10 @ Schwarzschild BH of 106 M(numerical - , point mass analytical --)

SPH numerical calculation, βp =10 →, snapshots for 8 values of the timet= -335,-236,-138,-40,50,157,255,353

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Tidal heating & EM radiation

• If stellar orbit periastron rp < rt (βp >>1)⇒compression, shock wave, gas gets heated Eth ~ Gm*/r* ~1048(m*/m )2(r*/r )-1 erg

• kT ~ Gm*mp/r* ~ 1 (m*/m )(r*/r )-1 keV⇒ prompt X-ray flare/transient expected,

• Crossing time ∆t ~ r*/vp ~10 (m*/m )-1/6 (r*/r )3/2 M6-1/3 s

• Rad. opacity τT~ m*σT/4πmpR*2 ~1010 (m*/m )(r*/r )-2

• In a crossing time ∆t radiation can diffuse out from a depth D~(c ∆t R*/τT )1/2 from the heated star

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X-ray flare types:• Prompt flare:

Lx,cs~(Eth/∆t)(c∆t/R*τT)1/2

≤1042 (m*/m )17/12(r*/r )1/4 M6-1/6 erg/s

∆tx ~∆t ~10 (m*/m )-1/6 (r*/r )3/2 M6-1/3 sec (→ Lx ∂ t-1/2 )

• Longer flare: disrupted gas falling back to rp suffers collisions (f0.1=f/0.1, coll. fraction):Lx,ve~ 1045 f0.1 M6

1/6 (m*/m )7/3 (r*/r )-5/2 erg/s∆tve ~ 10 M6 (m*/m )-1 (r*/r )3/2 dy ( → Lx,ve ∂ t-5/3 )

• Longest Flare: accretion, Lx,a ~3.1041erg/s, tviszk~103 yr(there are recent XMM observations claiming such a flare)

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Gravitational Waves

• Dimensionless strain h(perturbation of metric tensor), at distance D : h ~ (G/ D c4) dQ2/dt2 ~(Rg/D)(v/c)2

~ 2.10-22βp(D/10 Mpc)-1M62/3(m*/m) 4/3 (r*/r )-1

• Wave frequency: if βp =rt/rp = penetr. factor,f ~ (GMh/rp

3)1/2~6.10-4βp3/2(m*/m )1/2(r*/r )-3/2 Hz

⇒ LISA can measure it out to Virgo gal. cluster

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Solar type star, Mh=106 M , a=0

Average temperature @ periastron Gravitational strain from dist. D=20 Mpc,SPH: solid lines, point mass analyt: dash line

(Kobayashi, Laguna, Phinney, Mészáros,, astroph-O4O4173)

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↓ Helium star & ↓ Kerr BH

↑ He star, Schwarzschild BH a=0, βp=1, temperature (upper)gravitational strain (lower): pol. comp. h+: thick, hµ : thin

Solar type star, Kerr BH, a=1, βp=5. Progradre: solid, retrograde: dashedSPH: thick; point mass analyt: thin

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LISA• ESA/NASA collab.• 3 satelites in laser-

synchronized orbitstrailing the Earth

• MBH mergers, MBH-stellar disruption/swallow,

• Early Universe gravitational wavebackgrnd (inflation)

• Merger of large separation binaries

• Etc….

Laser Interferometer Space Antenna

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MBH mergers@ high z

• Polarization of GW could trace out LSS

• At reionization, feedback effects might be detectable

• LISA (10-4 -10-2 Hz), DECIGO,BBO (10-2 - 10 Hz)

Ioka, PM astroph/0502437

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SUMMARY• GRB are frequent events, with rich EM phenomenology,

good timing & position • Fairly well understood afterglow theory, but crucial

central engine/progenitor questions remain unresolved• GW signatures of GRB should be detectable,

aided by GW-EM coincid.; GW are potentially useful discriminants of progenitor candidates

• Massive BHs: stellar disruption involves both GW signatures of MBH mass & rotation rate, and EM flares