Primordial Black Holes in Cosmology Lecture 4: Accretion physics - - PowerPoint PPT Presentation

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Primordial Black Holes in Cosmology Lecture 4: Accretion physics Massimo Ricotti (University of Maryland, USA) Institute of Cosmos Sciences, University of Barcelona 23/10/2017 Astrophysical Constraints Microlensing Macho, EROS, etc

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Primordial Black Holes in Cosmology Lecture 4: Accretion physics

Massimo Ricotti (University of Maryland, USA)

Institute of Cosmos Sciences, University of Barcelona 23/10/2017

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Astrophysical Constraints

Institute of Cosmos Sciences, University of Barcelona

  • Microlensing
  • Macho, EROS, etc
  • UCMHs: lensing, astrometry, DM annihilation
  • Dynamical constraints
  • Power spectrum
  • Dynamical heating (halo binaries and dwarfs)
  • Gravitational waves from binary PBHs
  • Capture
  • Primordial binaries
  • Effects on CMB and reionization
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Collaborators: Jerry Ostriker (Princeton), Katie Mack (Princeton)

Physics Coll. Virginia Tech, 02-08-2008 – p.2/37

Institute of Cosmos Sciences, University of Barcelona

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Physics of PBHs accretion: Outline

Gas accretion onto PBHs produce X-rays and affect the ionization history of the IGM

  • 1. Growth of “clothing” dark matter halo (100-1000 times

more massive than PBH)

  • 2. Gas viscosity: Compton Drag and Hubble flow
  • 3. Proper motion: gas and dark matter are not perfectly

coupled (Silk damping)

  • 4. Angular momentum of accreted gas and dark matter
  • 5. Feedback processes (global and local radiative

feedbacks)

Physics Coll. Virginia Tech, 02-08-2008 – p.12/37

Institute of Cosmos Sciences, University of Barcelona

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  • 1. Clothing Dark Matter Halo
  • 1. PBHs seed accumulation of dark halo (fpbh < 1)
  • 2. The gas accretion rate onto the PBH is increased!

Ref: Mack, Ostriker and Ricotti (2007)

growth of order unity during radiation era Mh = 3Mpbh 1+z

1000

−1 Self-similar secondary infall solution (e.g., Bertschinger 1985) Truncated power-law density profile with α = −2.25 Truncation at rh = rta/3

Physics Coll. Virginia Tech, 02-08-2008 – p.13/37

Institute of Cosmos Sciences, University of Barcelona

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  • 2. Bondi type accretion

Spherical accretion (√) Steady-state (M < 2 × 104 M, √) Viscosity (Compton drag) dv dt = −4 3 xeσTUcmb mpc v = −βv Hubble expansion (M > 2 × 104 M, √) Clothing dark halo (power-law density profile, √)

Ref: Ricotti (2007)

Physics Coll. Virginia Tech, 02-08-2008 – p.14/37

Institute of Cosmos Sciences, University of Barcelona

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Spherical accretion rate

point mass potential (dashed curves) dark halo poten- tial (solid curves)

Physics Coll. Virginia Tech, 02-08-2008 – p.15/37

Institute of Cosmos Sciences, University of Barcelona

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  • 3. Relative motion of PBHs and gas

˙ Mg ∝ M 2 v3

eff

where veff = (v2

rel + c2 s)1/2

  • 1. Linear regime: Silk damping (i =baryons, dark matter)

Vi2 = Ω1.2

m H2

2π2 ∞ Pi(k)w2

s(k, a)w2 l (k, r0)dk,

σi2 = Ω1.2

m H2

2π2 ∞ Pi(k)w2

s(k, a)[1 − w2 l (k, r0)]dk.

  • 2. Non-linear regime: capture by mini-halos

Physics Coll. Virginia Tech, 02-08-2008 – p.16/37

Institute of Cosmos Sciences, University of Barcelona

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Physics Coll. Virginia Tech, 02-08-2008 – p.17/37

Institute of Cosmos Sciences, University of Barcelona

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Angular momentum of accreted material

Dark matter: Quasi-spherical accretion

  • Ang. momentum sufficiently large to avoid direct

accretion of DM into PBH Gas: Spherical accretion for M < 500 M Compton drag reduces further ang. momentum (Loeb 93; Umemura et al 93)

Physics Coll. Virginia Tech, 02-08-2008 – p.18/37

Institute of Cosmos Sciences, University of Barcelona

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  • 4. Accretion rate neglecting feedback

curves from bottom to top refer to masses of PBHs from 0.1 M to 105 M (factor of 10 spacing).

Physics Coll. Virginia Tech, 02-08-2008 – p.19/37

Institute of Cosmos Sciences, University of Barcelona

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  • 4. Accretion rate neglecting feedback

curves from bottom to top refer to masses of PBHs from 0.1 M to 105 M (factor of 10 spacing).

Physics Coll. Virginia Tech, 02-08-2008 – p.19/37

Institute of Cosmos Sciences, University of Barcelona

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Accretion Luminosity

Define dimensionless luminosity l = L/LEd and accretion rate ˙ m = ˙ M/ ˙ MEd, then: l = ˙ m, where is the radiative efficiency We assume: l = 0.01 ˙ m2 if ˙ m < 1 (spherical accretion) l = fduty(0.1 ˙ m) < fduty if ˙ m > 1 (thin disk)

Physics Coll. Virginia Tech, 02-08-2008 – p.20/37

Institute of Cosmos Sciences, University of Barcelona

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  • 5. Feedback processes

Local feedbacks (typically negligible) Size of H II region with respect to Bondi radius: In most cases rH II/rB < 1 If rH II/rB > 1 lt = l 1 + toff/ton = l 1 + (rH II/rB)1/3 = fdutyl Temperature of H II region: TH II ∼ Tcmb Global feedback (X-ray heating): Iterative semi-analytic code (Ricotti & Ostriker 04)

Physics Coll. Virginia Tech, 02-08-2008 – p.21/37

Institute of Cosmos Sciences, University of Barcelona

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Cosmic ionization, thermal, and chem- ical history

Simulations: Mpbh = 100, fpbh = 10−4

Physics Coll. Virginia Tech, 02-08-2008 – p.22/37

Institute of Cosmos Sciences, University of Barcelona

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Cosmic ionization, thermal, and chem- ical history

Simulations: Mpbh = 1000, fpbh = 10−7

Physics Coll. Virginia Tech, 02-08-2008 – p.22/37

Institute of Cosmos Sciences, University of Barcelona

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Cosmic ionization, thermal, and chem- ical history

Simulations: Mpbh = 1000, fpbh = 10−6

Physics Coll. Virginia Tech, 02-08-2008 – p.22/37

Institute of Cosmos Sciences, University of Barcelona

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Effects of PBHs on CMB anisotropies

Affects recombination Complementary and uncorrelated to reionization effects Affect small angu- lar scales: l>10

Physics Coll. Virginia Tech, 02-08-2008 – p.28/37

Institute of Cosmos Sciences, University of Barcelona

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Modified recombination history

xe(z) = xe,rec(z) + min

  • xe0

1 + z 1000 −1 , 0.1

  • ,

Created using CosmoloGUI

2 4 6 8 10 0.2 0.4 0.6 0.8 1 xe 104 Probability

RECFAST: Seager, Sasselov & Scott 99; COSMOMC: Lewis & Bridle 02

Physics Coll. Virginia Tech, 02-08-2008 – p.29/37

Institute of Cosmos Sciences, University of Barcelona

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Created using CosmoloGUI

xe 104 ! 2 4 6 8 10 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Physics Coll. Virginia Tech, 02-08-2008 – p.30/37

Institute of Cosmos Sciences, University of Barcelona

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Created using CosmoloGUI

xe 104 zre 2 4 6 8 10 8 10 12 14 16 18

Physics Coll. Virginia Tech, 02-08-2008 – p.30/37

Institute of Cosmos Sciences, University of Barcelona

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Created using CosmoloGUI

xe 104 ns 2 4 6 8 10 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

Physics Coll. Virginia Tech, 02-08-2008 – p.30/37

Institute of Cosmos Sciences, University of Barcelona

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Created using CosmoloGUI

xe 104 log(1010 As) 2 4 6 8 10 20 22 24 26 28 30 32 34

Physics Coll. Virginia Tech, 02-08-2008 – p.30/37

Institute of Cosmos Sciences, University of Barcelona

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New constraints on fPBH and β

Physics Coll. Virginia Tech, 02-08-2008 – p.31/37

Institute of Cosmos Sciences, University of Barcelona

Ricotti, Ostriker, Mack 2008

Results (2008)

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New constraints on fPBH and β

Physics Coll. Virginia Tech, 02-08-2008 – p.31/37

Institute of Cosmos Sciences, University of Barcelona

Ricotti, Ostriker, Mack 2008

Results (2008)

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wide binaries u l t r a

  • f

a i n t d w a r f s micro-lensing

R O M

Planck (strong feedback)

  • /⊙

()

Planck (no feedback) Ali-Haimoud and Kamionkowski 2016 (arXiv:1612.05644)

Results (2016)

Institute of Cosmos Sciences, University of Barcelona

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Horowitz 2016, (arXiv:1612.07264)

Results (2016)

Institute of Cosmos Sciences, University of Barcelona

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101 100 101 102 103

MPBH/M

108 107 106 105 104 103 102 101 100

fPBH

Accretion constraints Spherical accretion [57] Disk accretion with veff = cs,1 Disk accretion with veff = p cs,1hv2

Li1/2

Other constraints Micro-lensing [38] Radio [47] Dynamical heating of star cluster [40] Other constraints Micro-lensing [38] Radio [47] Dynamical heating of star cluster [40]

Poulin et al. 2017

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vB hv2

Li1/2

veff

  • (/)
  • see: Tseliakhovich and Hirata 2010,

Dvorkin, Blum, and Kamionkowski 2014

1) Effect of Supersonic Motions

Ali-Haimoud and Kamionkowski 2016 Ricotti, Ostriker, Mack 2008

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  • ϵ
  • no feedback

strong feedback 1

2

M

  • 1 M

104 M

2) Radiative Efficiency

Ali-Haimoud and Kamionkowski 2016

Institute of Cosmos Sciences, University of Barcelona

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  • 4. Accretion rate neglecting feedback

curves from bottom to top refer to masses of PBHs from 0.1 M to 105 M (factor of 10 spacing).

Physics Coll. Virginia Tech, 02-08-2008 – p.19/37

Institute of Cosmos Sciences, University of Barcelona

  • λ

no feedback strong feedback 102 M 1 M 104 M

  • 3) Accretion Rate
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  • 104M, fpbh = 104
  • Δ

103M, fpbh = 102 1

2

M

  • ,

f

p b h

= 1

Ali-Haimoud and Kamionkowski 2016

4) Other effects

  • Both new papers use a very

different approach for the effect ionizing radiation on the

  • IGM. Not clear if they are

consistent with each other.

  • Both seem to use methods that

have a significantly smaller effect on the ionization rate of Hydrogen than ROM.

  • Both new papers do not

consider the growth of DM halos around PBHs that can be significant at z<200

Institute of Cosmos Sciences, University of Barcelona

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  • H2016 used Planck with supersonic streaming motion.

Otherwise, accretion rate and efficiency are from ROM. Finds100% of DM in PBH if M<10Msun (ROM: M<1 Msun at 3 sigma)

  • AK2016 (strong feedback case) found similar limits as

H2016 but assuming significantly lower efficiency (and accretion rate?)

  • Both papers assumed spherical accretion for radiative

efficiency (as in ROM), but this is not consistent with PBHs moving supersonically at Mach ~5! An accretion disc will form.

General Comments on Revised Limits

Institute of Cosmos Sciences, University of Barcelona

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Institute of Cosmos Sciences, University of Barcelona

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Park & Ricotti 2013

Institute of Cosmos Sciences, University of Barcelona

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Park & Ricotti 2013

Institute of Cosmos Sciences, University of Barcelona

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Conclusions

  • New limits exclude 30 Msun PBHs as being >10% of the DM (ROM found 10-20

times more stringent limits: >0.5-1%)

  • Some inconsistencies appear to exist between new results that need to be better

understood

  • Assumption of spherical accretion for the radiative efficiency is no longer a valid

assumption given the supersonic motion and revised streaming motions

  • Even though the radiative efficiency is likely to be higher, other hydrodynamical

effects may reduce the accretion rate well below Bondi: radiation feedback, centrifugal barrier, to mention the most significant.

  • This type of modeling is messy, and to be certain we got it right we actually need

to detect an effect from PBHs rather than set upper limits: find a “smoking gun” using a combination of lensing, GWs, CMB and X-ray observations.

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Backup Slides

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Burst HII region formation Gas depletion Loss of Pressure Collapse

  • f dense

shell

Park & Ricotti 2011,2012

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Park & Ricotti 2013

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Bondi equations with viscosity        ˙ Mg = 4πr2ρv, v dv

dr

= − 1

ρ dP dr − GM(<r) r2

− β(z)v, P = Kργ.

Physics Coll. Virginia Tech, 02-08-2008 – p.34/37

Institute of Cosmos Sciences, University of Barcelona

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Bondi equations with viscosity in expanding universe    ˙ Mp = 4πx2(1 + δ)vp,

vp a ∂vp ∂x

= − 1

ρ dP adx − G[∆M(<ax)] (ax)2

− (β + H)vp Neglect gas self-gravity and βeff = (β + H) Steady-state: Hrb/cs,∞ < 1 → tcr < tH Transition to self-similar solution: MPBH > ∼ 2 × 104 M

Physics Coll. Virginia Tech, 02-08-2008 – p.34/37

Institute of Cosmos Sciences, University of Barcelona

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Point mass with viscosity (isothermal eos)

rb = GMbh c2

s,∞

, ˆ β = βeff rb cs,∞ λ = ˙ Mg 4πr2

bρ∞cs,∞

. λ = exp

  • 9/2

3 + ˆ β 0.75

  • x2

cr,

Physics Coll. Virginia Tech, 02-08-2008 – p.35/37

Institute of Cosmos Sciences, University of Barcelona

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Power-law halo with viscosity (isothermal eos)

ρ ∝ r−α → gdm(r) = −GMh r2 min[(r/rh)p, 1], p = 3 − α χ = rb/rh λh ≡ Υ

p 1−pλbh,

where, Υ =

  • 1 + 10ˆ

βh 1

10 exp (2 − χ)

χ 2 2 .

Physics Coll. Virginia Tech, 02-08-2008 – p.36/37

Institute of Cosmos Sciences, University of Barcelona

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Structure of the H II region

z = 500, S0 = 1052 ion. photons/sec νFν ∝ νβ β = 0.5 (Shapiro 73) t = 2, 100 and 4600 yr

TH II TCMB ≈ 1+ 0.36 β+2

1+z

1000

−2

Physics Coll. Virginia Tech, 02-08-2008 – p.37/37

Institute of Cosmos Sciences, University of Barcelona

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point mass potential (dashed curves) dark halo poten- tial (solid curves)

no feedback strong feedback 1 02 M 1 M 1

4

M

  • λ

λiso λad

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  • <>/

no feedback strong feedback 102 M 1 M 104 M

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0.5 1.0 5.0 10.0 50.0 100.0 10-5 10-4 0.001 0.01 0.1 1 MpbhêMü fpbh = WpbhêWCDM

xe0 < 3.3 × 105 (68% C.L.), xe0 < 7.0 × 105 (95% C.L.), ∆τe < 0.005 (68% C.L.), ∆τe < 0.012 (95% C.L.).

∆τe = 0.05 ✓Mpbh M ◆ f

1 2

pbh

Chen, Huang, and Wang 2016 (arXiv:1608.02174)