Agujeros negros de masa intermedia: efectos sobre su entorno y detectabilidad Pepe, Carolina 2013

Agujeros negros de masa intermedia: efectos sobre su entorno y detectabilidad Pepe, Carolina 2013 Tesis Doctoral Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires www.digital.bl.fcen.uba.ar Contacto: digital@bl.fcen.uba.ar Este documento forma parte de la colección de tesis doctorales y de maestría de la Biblioteca Central Dr. Luis Federico Leloir. Su utilización debe ser acompañada por la cita bibliográfica con reconocimiento de la fuente. This document is part of the doctoral theses collection of the Central Library Dr. Luis Federico Leloir. It should be used accompanied by the corresponding citation acknowledging the source. Fuente / source: Biblioteca Digital de la Facultad de Ciencias Exactas y Naturales - Universidad de Buenos Aires

UNIVERSIDAD DE BUENOS AIRES Facultad de Ciencias Exactas y Naturales Departamento de Física Agujeros negros de masa intermedia: efectos sobre su entorno y detectabilidad Tesis presentada para optar al título de Doctor de la Universidad de Buenos Aires en el área Ciencias Físicas Carolina Pepe Director de Tesis: Dr. Leonardo J. Pellizza Consejero de estudios: Dra. Cristina Caputo Lugar de Trabajo: Instituto de Astronomía y Física del Espacio (CONICET-UBA) Buenos Aires, 2013

M 10 2 10 4 M

10 2 10 4 M

W 0 8 m(r)/r ω ω

E(B V) 5000 K M BH =1000M M BH =3981M E(B V) 9976 K

E(B V) 12559 K ( P/P) ( P/P) int 2511M 3981M 100 M 1000 M

1 γ

M M 10 5 10 9 M

10 2 10 5 M 10 3 10 4 M M 10 9 10 M 10 5 M

jets scattering B 10 13 scattering B 10 12 L>10 40 erg s 1 10 3 10 5 10 6 M

Ṁ 10 4 M /t M t 30 M 100 M 10 2 10 3 M

M 250 M ω [1,3 2,3] 10 4 M 1000 M

ω 5 10 4 M 4,7 10 4 M 500M ω 4 10 4 M

ω 4,7 10 4 M 1,7 10 4 M 10 4 M [1,5 3,9] 10 3 M 3 10 3 M 2 10 3 M 2 10 3 M 8 10 3 M 6 10 3 M 800 M

140 M 2 10 4 M ( ) 0,6 ( L M F 5 =10 3 10 31 1 100 M ) 0,76 ( ) 2 d µ. 10

L M d L M cm 3 Ṁ L X = ǫṁc2 ǫ ω M ω M M

ω M ω M ω M M L X L X M M

M

2

10 5 10 6 M 100 10 8 10 10

f

f( r, v) d 3 rd 3 v d 3 r r d 3 v v Φ 2 Φ =4πG fd 3 v, 1 r d dr ( r 2dΦ ) =4πG dr fd 3 v, r f exp(e/σ 2 ) E σ

Φ 0 Ψ ε Ψ Φ+Φ 0 ε E +Φ 0 = Ψ 1 2 v2, v = v E Φ 0 f>0 ε > 0 f =0 ε 0

ρ 1 (2πσ 2 ) 2(e 3 ε/σ2 1) ε > 0 f K (ε)=. 0 ε < 0 ρ 1 9σ r 0 2, 4πGρ 0 ρ 0 ε > 0 2Ψ [ ( Ψ 1 ) ] 2 exp v2 1 v 2 dv 4π ρ k (Ψ)= (2πσ 2 ) 3 2 0 σ 2 ( ) Ψ 4Ψ = ρ 1 [e Ψ/σ2 erf σ πσ 2 ( 1+ 2Ψ ) ], 3σ 2 erf(x) Φ Ψ 1 r d dr ( r 2dΨ ) [ = 4πGρ 1 r 2 e Ψ/σ2 erf dr ( ) Ψ 4Ψ σ πσ 2 ( 1+ 2Ψ ) ]. 3σ 2 r =0 (dψ/dr)=0

Ψ r =0 Ψ(0) > 0 Ψ(0) Φ(0) (dψ/dr)=0 (d 2 Ψ/dr 2 ) < 0 Ψ 2Ψ r t r t M(r t ) Φ(r t ) Φ(r t )= GM(r t) r t. Φ(0) = Φ(r t ) Ψ(0) Ψ(0) Ψ(0) ρ 0 r 0 σ r 7/4

f ( E) 1/4 x r/r 0 ω v/σ W(x) Ψ(x)/σ 2 E ω 2 /2 W ν(x) ρ(x)/ρ 0 M (x) M(x)/ρ 0 r0 3 µ M/ρ 0 r0 3 r 0 σ ρ 0

c( E) 1/4 E< W f(e)= (2π) 3/2 (e E 1) W <E<0, 0 E 0 c (2π) 3/2 (exp(w ) 1)W 1/4 f W W(x t )=0 x t W W(x ) x M (x )=0,1µ, x GM/σ 2 r 0 M (x ) 10 4 µ x

W( ) d 2 W dx + 2 dw 2 x dx = (4πGρ 0r 2 σ 2 )ν(w), x>0; W 2W ν(w)=4π f(e)ω 2 dω = 0 ν 1, W W, ν 2, W>W ν 1 ν 2 W r 0 = 9σ2 4πGρ 0. d 2 W dx + 2 dw 2 x dx = 9ν(W), x>0, x 0 > 0

dw dx (x 0) = W 0, W(x 0 ) = W 0. x 0 = x W W dψ dr (x )= GM (x BH r 0 ) = Gµ ρ 2 x 2 0 r 0, W x = 9µ. 4πx 2 (µ,w ) 0,1 x x M (x) x x = GM/3σ 2 r 0 M =0,100,1000,4000 M W 0 8

r<r 0 100 sin IMBH M = 100 M # M = 1000 M # M = 4000 M # 1!/" 2 0.01 0.0001 0.001 0.01 0.1 1 10 100 r/r 0 W 0 8

0,8M 0,2M 0,1M α 10 14 10 11 1 10 3

10 100M H 2 M α 0,1 M 0,1M 10 2 10 5 M 5 10 4 M 9 10 4 M

M R m E acc = GMm/R, R 3 M M E acc 5 10 20 E nuc =0,007mc 2, c E nuc =6 10 18

g 1 M/R M/R Ṁ L Edd =4πGMm p c/σ T = 1,3 10 38 (M/M )erg s 1.

T =(L acc /4πR 2 σ) 1/4, σ R Sch =2GM/c 2 M 10 4 M ( ) 1/4 L Edd T = 3,8 10 6 K, 16πσG 2 M 2 kt 3 λ

v v T L λ v T ρ ρ t + (ρ v)=0 ρ v t +ρ( v ) v = P + f t (1 2 ρv2 +ρǫ)+ ( 1 2 ρv2 +ρǫ+p) v = f v F rad q P f q ǫ F rad ρ v T

r θ φ v T ρ θ φ v r = v 1 d r 2 dr (r2 ρv)=0. r 2 ρv ρ( v) Ṁ 4πr 2 ρ( v)=ṁ. f f r = GMρ/r 2 v dv dr + 1 dp ρ dr + GM =0. r 2 P = Kρ γ, K γ

γ γ =5/3 dp dr = dp dρ dρ dr = dρ c2 dr, c s ( ) 1 1 c2 d 2 v 2 dr (v2 )= GM [ ] 1 2c2 r. r 2 GM [ ] 1 2c2 sr GM c 2 s c 2 s(r ) d dr (v2 ) r v 2 <c 2 v 2 >c 2.

r s = GM/2c 2 s(r s ) v 2 = c 2 s d dr (v2 )=0 r s v 2 (r) v 2 (r )=c 2 s(r s ) v 2 r v 2 <c 2 s r>r s v 2 >c 2 s r<r s v 2 (r s )=c 2 s(r s ) v 2 r v 2 >c 2 s r>r s v 2 <c 2 s r<r s v 2 <c 2 s r v 2 >c 2 s r d dr (v2 )=0 r = r s d dr (v2 )=0 r = r s d dr (v2 )= v 2 = c 2 s(r s ) r>r s

d dr (v2 )= v 2 = c 2 s(r s ) r<r s r s r r r v 2 v>0 v<0

Ṁ v 2 2 + c2 s γ 1 GM r =. c 2 s(r )/(γ 1) c s (r ) c s (r s ) ( )1 2 2 c (r )=c ( ) 5 3γ Ṁ =4πr 2 ρ( v)=4πr 2 ρ(r )c (r ) c 2 s ρ γ 1 ρ(r s )=ρ(r ) [ ] 2/(γ 1) cs (r s ). c s ( ) [ ] (5 3γ)/2(γ 1) Ṁ = πg 2 2 ρ(r ) 2 M. c 2 (r ) 5 3γ

γ =1 γ 1 γ [ (5 3γ)/2(γ 1) 2 5 3γ] γ =5/3 e 3/2 γ =1 p ρ r c

ds 2 = ( 1 2M r ) ( dt 2 1 2M r ) 1 dr 2 r 2( dθ 2 +sen 2 θdφ 2). r,θ,φ M ds J µ ;µ =0, T µν ;µ =0, T µν =(ρ+p)u µ u ν pg µν, p = p(ρ) J µ = ρu µ

u µ ρur 2 = C 1 ( ) 2 P +µ (1 2mr ) ρ +u2 = C 2, µ = ρ + ǫ ǫ dρ du u [ 2V 2 ] m r ( 1 2m +u 2) + dr [ ] V 2 u 2 r 1 2m =0, +u r r 2 V 2 = dln(p +µ) dlnρ 1. r u u 2 = M/2r

V 2 = u 2 /(1 3u 2 ). V 2 u 2 > 1/3 r < 6M u µ T µν ;ν = u µ ρ,µ +(ρ+p)u µ ;µ =0. [ ρ ] ux 2 dρ exp = A, ρ ρ +p(ρ ) u<0 x = r/m ( (ρ+p) 1 2 ) 1/2 x +u2 x 2 u = C 1, r =2M

C 1 ( (ρ+p) 1 2 ) 1/2 [ ρ ] dρ x +u2 exp = C ρ ρ +p(ρ 2, ) C 2 = C 1 /A = ρ + p(ρ ) u = u(2m) ρ = ρ(2m) A 4 ρ +p(ρ ) ρ +p(ρ ) = A 2 [ 16u 2 (2M) =exp 2 ] dρ. ρ ρ +p(ρ ) ρ ρ ρ +p(ρ ) [ 1+3c 2 ρ +p(ρ ) (ρ ) ] [ ρ ] 1/2 dρ =exp. ρ ρ +p(ρ ) ρ r u Ṁ = 4πr 2 T0 r Ṁ =4πAM 2 [ρ +p(ρ )].

Ṁ ρ +p(ρ ) < 0

3

10

M ds 2 = e ν dt 2 e λ dr 2 r 2 (dθ 2 +sin 2 θdφ 2 ), r,θ,φ t ν λ r m(r) r m(r)=m ν = λ =ln(1 2M/r)

p = ωρ p ρ T µν =(ρ+p)u µ u ν pg µν, g µν u µ = dx µ /ds u µ u µ =1 Ṁ = 4π lím r 2M r2 T r 0, ρ p u =0 (p+ρ) ( e ν +e λ ν u 2) 1/2 ur 2 e 1 2 (λ+3ν) = C 1, e ρ dρ ρ +p e 1 2 (ν+λ) ur 2 = C 2, C 1 C 2 (p+ρ)e ρ dρ ( p+ρ 1+e λ u 2) 1/2 e ν/2 = ρ +p. ρ +p r

Ṁ = 4π(ρ +p )C 2, r 2M λ+ν =0 C 2 C 2 [ (e ν +e λ ν u 2 ) 1 e λ ν u ω ] du+ [ u 1 2 (e ν +e λ ν u 2 ) 1 ( e ν ν +(λ ν )u 2 e λ ν )+ λ 2 + 3ν 2 + 2 ( ν r (1+ω) 2 + λ 2 + 2 )] dr =0, r 1 2 ν (r c )(1 ω) 2ω r c =0, ν λ

u 2 c = ω 1 ω. ω < 0 ω > 0 ν (r)= 2m(r) r[r 2m(r)]. ν r c m(r c ) r c = 2ω 1+3ω. ω C 2 Ṁ = π(1+ω)ρ [ e νc (1+ ω ( )1 ω 1 ω 2 m 2 (r c )( 1+3ω ω ] 1 1 ω ) 2ω ) 2 e 1 2 νc. Ṁ m2 (r c ) M 2 (M gc + M) 2 M gc M gc M

r 0 r t c gc R gc M R gc ρ DM ρ DE 3000M 4,0 10 21 kg m 3 7,7 10 27 kg m 3 ω 10 K

p = ρ/3 ω r 0 =0,35 pc c gc =1,8 M =3000M r 0 M/r r/r 0 10

ω 1 m(r)/r r r 0 r c u c Ṁ M 2 ρ =7,0425 10 31 3 Ω = ρ ρ =5 10 5, ρ crit ρ =1,878 10 29 h 3, h =0,75 H 0 =7,5 10 7 1 1 Ṁ =1,7 10 29 M yr 1 Ṁ M(r)/r 0 r 0

1e-08 9e-09 8e-09 7e-09 0 20 40 60 80 100 120 140 1e-08 9e-09 8e-09 7e-09 m(r)/r 6e-09 5e-09 4e-09 6e-09 5e-09 4e-09 3e-09 2e-09 1e-09 0 0 20 40 60 80 100 120 140 r /r 0 3e-09 2e-09 1e-09 0 m(r)/r 2ω/(1+3ω) 700 1

ρ p = ωρ ω 1 ω ω 1,5 10 9 ω ω 5 10 10 m(r c ) M + M gc 3 10 9

r c ω > ω t =1,5 10 9 ρ = ρ DM c 2 ρ DM r c ω 3 10 10 r c r r

Ṁ(v) v Ṁ0 c 3 s Ṁ(v)=Ṁ0 (v 2 +c 2 3/2, s) c 2 s = c 2 ω ω 0 Ṁ(v) Ṁ0 v =0,100,200 M t 10Gyr ω 10 9 Ṁ m(r c ) r c r 0 M Ṁ t 104 M

1000 100 Solución interna Solución externa 10 r/r 0 1 0,1 0,01 0,001 1e 10 1e 09 1e 08 1e 07 ω ω Tasa de acreción (M sol /yr) 100 1 0,01 0,0001 1e 06 1e 08 1e 10 v = 0 v = 100 km/s v = 200 km/s v = 500 km/s 1e 12 1e 10 1e 09 1e 08 ω ω

v ω 10 9 10 9 ω < 1/3 ω = 1

ω < 0 r c < 2M Ṁ =16π(1+ω)ρ M 2. Ṁ ω < 1

ρ DE c 2 ρ ( ) 2 M Ṁ =9,5 10 34 M yr 1 (1+ω). M 10 2 10 4 M M =6,9 ± 0,9 M M =0,3 ± 0,2 M R =3R

U = 105 ± 16,V = 98 ± 16,W = 21 ± 10 1 v BH 140km/s 10

100 1 velocidad nula v = 145 km/s M acretada 0,01 0,0001 1e 06 1e 12 1e 10 1e 08 1e 06 ω 1 Factor de corrección 0,01 0,0001 1e 06 1e 08 1e 12 1e 10 1e 08 1e 06 ω

4 10 31 32 erg s 1

1arcsec 2 10 4 M

ρ = αρ ρ α 10 14 10 11 yr 1 λ 10 4 10 3 1 d r 2 dr (ρr2 u)=αρ,

r u ρ ρu du dr = k BT dρ µ dr GM(r)ρ αuρ, r 2 G k B µ M(r) r M BH q = q/α q = ρur 2 du dr = u u 2 c 2 s d q dr = ρ r 2, ( 2c 2 s r GM(r) ) (u2 +c 2 s)r 2 ρ, r 2 q c s = k B Tµ 1 α q = r 0 ρ r 2 dr + q 0 = M (r) 4π + q 0, q 0

ξ = rr 1 0 ψ = uσ 1 ψ s = c s σ 1 ω = q(ρ 0 r 3 0) 1 Ω (ξ)=m (r)(4πρ 0 r 3 0) 1 Ω BH = M BH (4πρ 0 r 3 0) 1 Ω(ξ)=Ω (ξ)+ Ω BH r 0 ρ 0 σ 2 =4πGρ 0 r 2 0/9 ω = Ω (ξ)+ω 0, dψ dξ = ψ ψ 2 ψ 2 s ( 2ψ 2 s ξ dω (ψs 2 +ψ 2 ) 9Ω(ξ) ). dξ ω ξ 2

ξ st u =0 Ω (ξ st )= ω 0, ξ st ξ st ξ st ξ s f (ξ)=2ψ 2 s ( 1 ξ 1 ) dω 9Ω(ξ) =0. ω dξ ξ 2

20 10 T = 9976 K T = 12559 K T = 15811 K f s 0-10 -20 0.1 1 10 100 r(r 0 ) T = 9976, 12559 15811 K M f (ξ) M T =9976, 12559 15811 K f s (ξ)=0 du/dr =0 ξ st ξ st T = 3,99, 4,09 4,19

ξ st ξ st ω c GC r 0 r 0 ρ 0 σ M(r) M(r) c s /σ Ω BH

σ r 0 ρ 0 c GC km s 1 pc M pc 3 10 5 10 5 ω 10 3 10 4 M/M L/L 5000 15000 K 10 2 10 4 M ξ st Ω (ξ st ) c s /σ Ω BH Ṁ Ṁ = αω (ξ st )ρ 0 r0 3 α c s /σ r st r 0 c s /σ 1

c s /σ 1 r st r 0 c s /σ < 1 r st r 0 c s /σ Ω BH

100 M 15 Liller 1 " Cen M 28 10 r st (r 0 ) 1 0.1 0 1 2 3 4 5 6 2 2 c s /! 100 10 M 15 Liller 1 $ Cen M 28 "#(r st ) 1 0.1 0 1 2 3 4 5 6 2 2 c s /! ω Ω BH

100 10 r st (r 0 ) 1 M 15 Liller 1 " Cen M 28 0.0001 0.001 0.01 0.1 BH 100 10!"(r st ) 1 0.1 M 15 Liller 1 # Cen M 28 0.01 0.0001 0.001 0.01 0.1! BH ω c 2 s/σ 2 1 3

10000 1000 M 15 Liller 1! Cen M 28 r st /r acc 100 10 1 100 1000 10000 M BH M M M r acc = GM BH /c 2 s M r st /r acc M BH Ṁ M2 BH

α α =10 11 yr 1 Ṁ r 0 ρ 0 M GC σ Ṁ σ M BH =1000M T =5000, 10000, 12600 K T =5000K M BH =1000, 4000, 10000M T σ c s /σ

σ Ṁ ρ 0r0 3 Ṁ r st M GC M GC Ṁ M GC ρ 0 r 3 0 σ

1e-05 Accretion rate (M Sun yr -1 ) 1e-06 1e-07 Liller 1 M 28 " Cen M 15 NGC 6388 1e-08 T = 5000 K T = 10000 K T = 12600 K!(m/s) 10000 1e-05 Accretion rate (M Sun yr-1) 1e-06 1e-07 1e-08 Liller 1 M 28 " Cen M 15 NGC 6388 M = 1000 M Sun M = 4000 M Sun M = 10000 M Sun! (m/s) 10000 σ M M M Ṁ σ σ

1e-05 T = 5000 K T = 10000 T = 12300 K Accretion rate (M Sun yr -1 ) 1e-06 1e-07 Liller 1 M 28 NGC 6388 M 15! Cen 1e-08 0 5e+05 1e+06 1.5e+06 M GC (M Sun ) 1e-05 M = 1000 M Sun M = 4000 M Sun M = 10000 M Sun Accretion rate (M Sun yr -1 ) 1e-06 1e-07 Liller 1 M 28 NGC 6388 M 15! Cen 1e-08 0 5e+05 1e+06 1.5e+06 M GC (M Sun ) M M M M GC

M GC 398 M 1000 M 3981 M M 9976 K r est

10000 100 M = 0 M = 398 M Sol M = 1000 M Sol M = 3981 M Sol! 1 0.01 0.0001 0.01 1 100 r (r 0 ) 0 u (!) -5 0 50 100 r (r 0 ) M = 0 M = 398 M Sol M = 1000 M Sol M = 3981 M Sol r est

r est f s (ξ)=0 ξ

r est r t P t = ρ(r t )c 2 s. r est R z n (R,z)= [ ( )] ( ) z 2 2,5+1,5exp 10 4 m 3, 70 pc 1+ R R 0 R 0 =8kpc n α

T =100K P = nkt, k r est r est

P ext r est r est P t P marea r est P t α ρ α r est Ṁ T =9976K r est

1e-12 1e-13 T = 5000 K T = 9976 K T = 15811 K P ext P marea (Pa) 1e-14 1e-15 1e-16 1e-17 1 10 100 r est (r 0 ) 1e-14 1e-15 M = 398 M Sol M = 1000 M Sol M = 3981 M Sol P ext P marea (Pa) 1e-16 1e-17 1 10 100 r est (r 0 ) M M M M

u T = 10000 K ṀEdd = L Edd /c 2 c L Edd =1,26 10 38 (M BH /M )ergs 1 Ṁ BH =4πG 2 M 2 BH ρ ac 3 s ρ a ρ a =0,2cm 3

1e+06 10000 M = 398 M Sol M = 1000 M Sol M = 3981 M Sol 100! 1 0.01 0.0001 0.01 1 100 r (r 0 ) 0.5 M = 398 M Sol M = 1000 M Sol M = 3981 M Sol u (c s 2 ) 0-0.5 0 20 40 60 80 100 120 r (r 0 ) r est

α ρ a α 10 14 10 11 yr 1 MBH 2 Ṁ

0.0001 Accretion rate (M Sun yr -1 ) 1e-08 1e-12 M 15 Liller 1! Cen M 28 Eddington limit Bondi-Hoyle 100 10000 M bh (M Sun )

1e-05 Tasa de acrecion (M Sol yr -1 ) 1e-06 1e-07 1e-08 1e-09 M = 398 M Sol M = 1000 M Sol M = 3981 M Sol 1e-10 0.01 1 100 r(r 0 ) M α = 10 11 yr 1 Ṁ M α =10 11 yr 1

L X α ǫ = L X /Ṁc2 ǫ =0,1 α =10 11 yr 1 10 37 10 41 erg s 1 10 32 10 41 erg s 1 10 38 40 erg s 1 L X, NGC6388 =2,7 10 33 erg s 1 L X, NGC6388 =8,3 10 32 erg s 1 α ǫ

T M BH M T =9976K α =10 11 yr 1 L X, NGC6388 α 10 11 10 14 yr 1 L X 10 31 erg s 1 ǫ = Ṁ/ṀEdd, Ṁ<0,1ṀEdd ǫ =0,1 ǫ =0,001

1e+42 1e+40 L X (erg s -1 ) 1e+38 1e+36 1e+34 1e+32 M = 100 M Sol M = 10000 M Sol 0.001 0.01 0.1 1 10 r est (r 0 ) ǫ =0,001 ǫ =0,1 M M α =1 10 11 yr 1

ρu du dr = dp dr ρdφ dt αuρ, φ dρ dr = ρ d ( ) P + P dρ dr ρ ρ dr, c 2 s γ P ρ γ = c p /c v c p c v

( ) ( ) u 1+ c2 s du dc 2 γu 2 dr = 1 s γ dr + c2 s dq q dr 2c2 s dφ r dr αρ r 2 u. q h = u2 2 + γ P γ 1 ρ +φ = u2 2 + c2 s γ 1 +φ, 1 d r 2 dr (qh)=αρ (ǫ+φ), ǫ h = ǫ+ α q r r ρ r 2 φdr. r est q =0 r>r st c 2 s c 2 s du dr = 1 ( u ) 1 c2 s u 2 [ (γ 1) d ( )] dr (h φ)+2c2 s r γdφ dr αρ r 2 u 2 c 2 s q u +γ. 2

ω = Ω (ξ)+ω 0, dψ dξ = 1 ( ψ ) 1 ψ2 s ψ 2 [ (γ 1) d dr (had φ ad )+ 2ψ2 s ξ γ dφad dξ dω/dξ ( )] ψ 2 s ω ψ +γ. 2 φ ad = φ/σ 2 h ad = h/σ 2 T =4000K R =70R M =0,8 M v e 35km s 1 ǫ = k T m +0,5v 2, k b m H

T ef ǫ = k bt ef m H. 15km s 1 T ef [10 4 10 5 ]K T ef q d(qh) dr = q dh dr =0. h = h t h t φ(r) M cum +M BH

φ =0 c 2 s = dp/dρ T 100 K T 0 T << T ef c 2 s u =0 h t h t =0 r est r<r est f s (ξ) f s (ξ)= (γ 1) d dr (had φ ad )+ 2ψ2 s ξ γ dφad dξ dω/dξ ( ψ 2 s ω ψ 2 +γ ). f s (ξ)

7 6 5 T = 100000 K T = 50811 K T = 10000 K T = 2000 K T = 1000 K 4 f s 3 2 1 0 0 2 4 6 8 10 r(r 0 ) f s (ξ) 1 10 3 2 10 3 1 10 4 5 10 4 1 10 5 K M 1 10 3 2 10 3 1 10 4 5 10 4 1 10 5 K M f s =0 r<r est T 2 10 3 K ξ int son

r est T 30000K f s (ξ)=0 ξ < ξ tidal f s (ξ)=0 h ρ 0 f s (ξ)= dφad dξ + (had tidal φad ) ξ, c 2 s = (h ad t φ ad )/2 dφ ad /dr = φ ad /r h ad t ξ =0. ξ h t =0 u dψ/dξ =0 ξ > ξ marea u =0 ξ

5

m λ

m λ0 A V = V V 0. E B V =(B V) (B V) 0. A λ = m λ E B V =(B B 0 ) (V V 0 )=A B A V. A λ λ R λ R λ = A λ /E(B V). E(B V) R λ

R λ R V R V 3,1 R V R V ν ǫ ν ǫ ν dω

dω I ν I ν dω dω l l + dl ǫ ν dωdl I ν κ ν I ν dωds κ di ν ds = κ νi ν +ǫ ν. ǫ ν =0 I ν,0 ( s ) I ν (s )=I ν,0 exp κ ν ds, 0 s T ν

κ ν = nσ e, σ e n = ρ polvo /m polvo 10 3 ρ gas ρ gas a q σ e = qπa 2. I ν = I ν,0 exp σe s 0 n(s)ds. I ν m m = 2,5logI ν +cte 1 µm

(I X0 exp s m m 0 = X X 0 = 2,5log s = 2,5log(exp κ X ρ(r)ds) s = 2,5log(exp σ e,x n(r)ds) 0 0 I X0 0 κ X(s)ρ(r)ds ) m 0 σ A λ A λ =1,08σ λ e s 0 n(r)ds. A V A λ A V = σ e,λ σ e,v. s s E λ V =1,08σ e,λ n(s)ds 1,08σ e,v n(s)ds =1,08 =1,08 =1,08 0 s 0 s 0 s 0 n(s)ds(σ e,λ σ e,v ) n(s)ds σ e,v ( σ e,λ σ e,v 1) n(s)ds σ e,v ( A λ A V 1). 0

A λ /A V R V A λ /A V = a(x)+b(x)/r V, x = λ 1 λ µm 1 a(x) b(x) A λ /A V E(B V) 0,1 r 0 4 r 0 4 r 0 r p 1µm m p 10 14 g q =0,1 s

senθ p p R t z T =5000,9976 12559 K M BH =0,398,1000 3981 M E(B V) E(B V) T =5000K T 10000K R t z

E(B V) 5000 K M = 398 1000 M

M BH = 1000 M M BH = 3981 M

E(B V) 9976 K M = 398 1000 3981 M T = 5000 K

M BH = 1000 M M BH = 3981 M

10 2 M BH 10 3

max{e(b V}) 1,32 10 6 1,13 10 7 5,52 10 5 1,38 10 7 E(B V) 1000 M T =9976K NGC 6681 100 M M BH 600 M

E(B V) 12556 K M = 398 1000 3981 M T = 5000 K

M BH = 1000 M M BH = 3981 M

10 17 kg m 3 p+e n+ν. ρ c =3,210 14 kg m 3 R 10 6 cm

ρ > 10 11 kg m 3 P 10 15 s 1 P/ P 10 7 yr

http : //www.naic.edu/pfreire/gcpsr.html

P<0 r 3 r 0 P P int a l a l P int a s a G

π r c R T a a l a c ( P/P) = a c + a c + a c + ( P/P), P a a c = µ2 D c, D c µ

a GM φ 1 (R,z) = 1 {R 2 +[a 1, +(z 2 +b 2 1 )1/2 ] 2 } 1/2 GM φ 2 (R,z) = 2 {R 2 +[a 2, +(z 2 +b 2 2 )1/2 ] 2 } [ ( ) 1/2 ( )] φ 3 (r) = GMc 1 ln r c 1+ r2 + r r 2 r c arctan r c, R r r 2 c a s a G ( P/P) obs ( P/P) a l a c

τ ( P/P) = P/(2 τ). ( P/P) a(r) a l a l = a θ = a r ((R T /r)), R T a l (r) M =1000M R T r z z ( P/P) int ( P/P) =( P/P) a c ( P/P) =( P/P) a c,

Rt = 0.94 r 0 Rt = 0.27 r 0 a normal (! 2 /r 0 ) 0.4 0.3 0.2 0.1 0 0 20 40 60 80 100 r (r 0 ) M ( P/P) < ( P/P) < ( P/P) ( P/P)

P/P int (s 1 ) 1,4 10 18 1,43 10 18 1,66 10 18 1,47 10 18 1,33 10 18 1,41 10 18 1,29 10 18 P/P int

Variacion intrinseca (s -1 ) 6e-17 4e-17 2e-17 0-2e-17-4e-17 47 Tuc Minimo Maximo Variacion intrinseca (s -1 ) 6e-17 4e-17 2e-17 0-2e-17 47 Tuc Minimo Maximo -4e-17-6e-17 0 2 4 6 8 10 12 14 Pulsar # -6e-17 0 2 4 6 8 10 12 Pulsar # Variacion intrinseca (s -1 ) 5e-17 0-5e-17 NGC 6440 Minimo Maximo Variacion intrinseca (s -1 ) 5e-17 0 NGC 6440 Minimo Maximo -5e-17 0 1 2 3 4 5 6 Pulsar # 0 1 2 3 4 5 6 Pulsar # 1.5e-16 NGC 6441 Minimo Maximo 1.5e-16 NGC 6441 Minimo Maximo Variacion intrinseca (s -1 ) 1e-16 5e-17 0 Variacion intrinseca (s -1 ) 1e-16 5e-17 0-5e-17-5e-17-1e-16-1 0 1 2 3 4 Pulsar # -1 0 1 2 3 4 Pulsar # ( P/P) int P/P

2e-16 2e-16 M 62 Minimo Maximo M 62 Minimo Maximo Variacion intrinseca (s -1 ) 1e-16 0-1e-16 Variacion intrinseca (s -1 ) 1e-16 0-1e-16-2e-16-2e-16-1 0 1 2 3 4 5 6 Pulsar # -3e-16-1 0 1 2 3 4 5 6 Pulsar # 3e-16 3e-16 2e-16 M 15 Minimo Maximo 2e-16 M 15 Minimo Maximo Variacion intrinseca (s -1 ) 1e-16 0-1e-16 Variacion intrinseca (s -1 ) 1e-16 0-1e-16-2e-16-3e-16-2e-16-4e-16-3e-16-1 0 1 2 3 4 5 6 7 8 Pulsar # -5e-16-1 0 1 2 3 4 5 6 7 Pulsar # 2e-15 Variacion intrinseca (s -1 ) 1e-16 0-1e-16 NGC 6752 Minimo Maximo Variacion intrinseca (s -1 ) 1e-15 0-1e-15 NGC 6752 Minimo Maximo -1 0 1 2 3 4 5 Pulsar # -2e-15-1 0 1 2 3 4 5 Pulsar # ( P/P) int P/P ( P/P) int < 0

DM z ρ(r) z DM cum DM DM = DM cum + z z n e (r(z ))dz. α DM cum ( P/P) int χ 2 = N P 1 (DM DM) 2 DM 2, ( P/P) int α

P DM obs DM χ 2 R T z z

225 224 T = 5000 K T = 9976 K T = 12559 K 224 T = 5000 K T = 9976 K T = 12559 K 223 223 DM (pc cm -3 ) 222 221 DM (pc cm -3 ) 222 221 220 219 0.06 0.08 0.1 0.12 0.14 R t (arcmin) 220 0.06 0.08 0.1 0.12 0.14 R t (arcmin) 100 M R t z

24.44 24.42 DM (pc cm -3 ) 24.4 24.38 24.36 24.34 24.32 0 0.05 0.1 0.15 0.2 0.25 0.3 Rt (arcmin) 100 1000 M M BH 100 M M 6000 M 3981 6309 10000 M α [10 14 8 10 12 ]yr 1 1000 M

116 115.5 T = 5000 K T = 9976 K T = 12559 K DM (pc cm -3 ) 115 114.5 114 113.5 113 0 0.1 0.2 0.3 0.4 Rt (arcmin) 2511 M R t z

67.4 67.4 67.35 T = 5000 K T = 9976 K T = 12559 K 67.35 T = 5000 K T = 9976 K T = 12559 K 67.3 67.3 DM (pc cm -3 ) 67.25 67.2 DM (pc cm -3 ) 67.25 67.2 67.15 67.15 67.1 0.015 0.02 0.025 0.03 0.035 0.04 R t (arcmin) 67.1 0.015 0.02 0.025 0.03 0.035 0.04 R t (arcmin) 67.4 67.35 T = 6294 K T = 9976 K T = 12559 K DM (pc cm -3 ) 67.3 67.25 67.2 67.15 67.1 0.015 0.02 0.025 0.03 0.035 0.04 R t (arcmin) 3981 M 6309 M 10000 M M 6000 M

33.36 33.34 T = 5000 K T = 9976 K T = 12559 K 33.35 T = 5000 K T = 9976 K T = 12559 K DM (pc cm -3 ) 33.32 33.3 33.28 DM (pc cm -3 ) 33.3 33.25 33.26 33.24 33.2 0.1 0.15 0.2 0.25 Rt (arcmin) 0.08 0.1 0.12 0.14 0.16 0.18 0.2 R t (arcmin) 100 M 1000 M M BH 100 M

6

ω 10 9 ω

r est r 0

E(B V)