Low Frequency Gravitational Waves from the Galactic Halo - - PowerPoint PPT Presentation

Low Frequency Gravitational Waves from the Galactic Halo

Investigating the nature of the MACHOs

Shane L. Larson

Space Radiation Laboratory California Institute of Technology Sources & Data Analysis Workshop Pennsylvania State University 29 October 2002

THE STORYLINE

• Recollection of microlensing
• MACHOs and the dark halo (EM)
• Gravitational waves from MACHOs

» High frequency » Low frequency BH MACHOs » Low frequency WD MACHOs

• Questions

LENSING

True Position Apparent Postion Deflector Mass

q

Lens Mass Image 1 Image 2 Lens

A B C A B C time amplification EINSTEIN RADIUS

RE = 4GM c2 D

AMPLIFICATION

A = u2 + 2 u u2 + 4 GRAVITATIONAL MICROLENSING

• If the angular separation of the

images is too small to be resolved microlensing occurs

• Microlensing amplifies the light;

how much depends on the impact parameter with lens

THE MACHO SEARCH

• The MACHO Collaboration

monitored 11.7 million stars in the Large Magellanic Cloud, on a regular basis, for 5.7 years

• Detected 13-17 mlens events
• MACHO mass: m ~ 0.5 MO
• Halo Fraction: ~8% – 50%,

depending on halo model

• ~ 2 x 1011 MACHOs out to

50 kpc

.

MACHOs @ HIGH FREQUENCY

• [1996] Nakamura, Sasaki, Tanaka & Thorne assume MACHOs

are primordial black holes, approximate a distribution to estimate coalesence rate » (50 kpc halo) ~ 5 x 108 binaries, ~ 5 x 10-2 yr-1 gx-1 » (300 kpc halo) ~ 3 x 109 binaries, ~ 0.3 yr-1 gx-1

• [grqc/9609027 (OMNI-I)] Finn estimates 30% of MACHOS are

binaries

• Coalesence rate: 15 yr-1 gx-1
• Suggest LIGO I could detect these to 15 Mpc (Virgo), so

might see several per year

• LIGO II could detect these to 150 Mpc, so could still see

several per year even if rate is 10-5 yr-1 gx-1

HILS BENDER GALACTIC BACKGROUND

Bender & Hils, CQG 14, 1439 (1997) Hils, Bender & Webbink, ApJ 360, 75 (1990)

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log hf (per ÷Hz)

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log f (Hz)

LISA AM CVn Binaries Hils-Bender Disk WD

BH MACHOs at LOW FREQUENCY

• Ioka et al. [2000] considered extracting galactic halo

structure from BH MACHOs with LISA: core radius, triaxiality etc to within ~10%

• Catch: 700 individual binaries, 10 yrs of observations
• [1998] Hiscock assumed the NSTT binary distribution

function and evolved to present time

• Generates the distribution in the current epoch

evolving only under gravitational radiation

• Analysis by Ioka et al. [1999] obtain similar spectra

BH MACHO GALACTIC HALO

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log hf (per ÷Hz)

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log f (Hz)

LISA bh Halo (Wh2 = 1.0) bh Halo (Wh2 = 0.1)

Hiscock, ApJ 509, L101 (1998) Ioka et al, PRD 60, 083512 (1999)

WHITE DWARF MACHOs?

• For a long time, WD had been discounted as halo
• bjects — searches for dim red stars found none
• Recent cooling models (Hansen, ApJ, 520, 680 [1999]; Saumon &
• Jacobson, ApJ, 511, L107[1999]) suggest WD form molecular

hydrogen atmospheres, absorb red light

• New observing campaigns have turned up WD

halo candidates (Ibata et al, ApJ, 524, L95 [1999]; Ibata et al,

• ApJ, 532, L41 [2000]; Oppenheimer et al, Science, 292, 698 [2001])
• Operate on assumption that there are WD in halo.

Simplest assumption possible: mimic the disk.

Scaling the Disk to the Halo

• Simply take the disk distribution and mulitply by

a scaling function:

• N and ·d-2Ò can be computed from distributions
• Key unknown parameter is a:

[ ]

1/2 K(a) = a Nhalo ·d-2Òhalo Ndisk ·d-2Òdisk hf = K(a) hf

h a l

• d

i s k

a = fraction of WD in binaries in halo

fraction of WD in binaries in disk

• When the scale factor K(a) > 1, halo is brighter than disk
• If small relative fractions of halo WD are binary (~1%),

the halo will stand out from the disk

• When a = 1, the WD binary fraction is equal in the halo

and the disk, and the scale factor is

a > 10-2

50 kpc halo

a > 5 x 10-3 300 kpc halo

K(1) = 5.42 50 kpc halo K(1) = 5.49 300 kpc halo

Binary Fraction Ratio: a

WHITE DWARF GALACTIC HALO

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log f (Hz)

LISA wd Halo (300 kpc) wd Halo (50 kpc)

Hiscock, Larson, Routzahn & Kulick, ApJ 540, L5 (2000)

• The real outstanding questions about the halo:

» What's the other 50%? » What in the blazes are the MACHOs?

• What about GW from the halo?

» BH — is there a better distribution? » WD — is there a better distribution? » Other Exotics — boson stars?

• EM astronomy undoubtedly has more to say

» Deep halo observing campaign? » Can it be done from archival data?

What now?