Primordial backgrounds -- from Gravitational Wave Observations or - - PDF document

There is a stochastic gravitational radiation background

PSU GWPW 11/2001

Primordial backgrounds

• from Gravitational Wave Observations
• r

``That which is static and repetitive is boring. That which is dynamic and random is confusing. In between lies art.''

John A. Locke

Steinn Sigurdsson Department of Astronomy & Astrophysics Penn State sources that either have individual h « h , but, N h ~> h

s min 1⁄2 s min

• r sources that could be distinguished individually, but have ``pile-up'', sources unresolved in frequency due

to finite Delta f Ļ t (~ 10 ) for t ~ 10 s and f ~ 10 Hz

• bs

5

• bs

8

• 3

Redshift: h strong f dependence - shift many high-z strong sources into local lower f waveband, cause confusion. Issues: gaussian or non-gaussian statistics of sources resolve through polarization or directional information filter out through optical matching integrate for longer time! left with irreducable background + noise There is science in the background, and we want to get to the cosmological primordial background - so understand other background. Would we know it if we saw it?

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Lots of good comprehensive Monte-Carlo models of populations. Large systematic uncertainties (use GW to set true parameters!) So we consider simple numbers: If we saw pure Gaussian noise with some power in a single interferometer, would we know to accept it as detection of the cosmological background? Especially if it is not where the standard model predicts it? If we see a (non-gaussian) background, can we tell it is not a cosmological background but astrophysical foreground?

Footnote: from the meeting discussion, let me repeat the issue. If LISA were to detect some sources, and after subtraction of strong point sources, the galactic foreground, and the modeled extragalactic background. And then, if after Sagnac calibration of the instrumentation noise, we saw, say, a broadband gaussian noise, peaking at, say, 27 mHz, and a paper was published claiming a detection of broken primordial spectrum in accordance with some beyond-the-Standard-Model theory (say a Brane inspired LED theory at some particular energy), THEN, would anyone believe the result? I'd contend, ``no'', they would not. Tuck Stebbins made a good analogy here with the neutrino deficit detections. There the results were really ``believed'' after a couple of decades of confirmation, including independent detection by detectors operating at different energies using different technology. Still a breakthrough result, but the way in which such tentative single data point results get accepted is indicative.

• Model astrophysical sources.
• Sagnac calibration to determine instrument noise, or cross-correlation of two (or more) interferometers

Model galactic foreground Extrapolate to Extragalactic Background Figure if there has been significant z-evolution Add it up ``Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.''

• J. von Neumann

~ 10 stars per galaxy

11

~ 10 galaxies (for suitable value of ``galaxy'')

10

Volume of universe is ~ 10 Mpc

11.5 3

~ 10 stars become white dwarfs

• 1

~ 10 stars become supernova

• 3

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~ 10 stars become black holes

• 4

Inject some initial distribution of periods, masses. Current in f, df/dt space - is it a stationary state with no evolution (boring!), a rapidly merging population with input balancing output, or bridging population with bunching at t ~ T ?

GW H

Non-gaussianity: if eccentric orbits, power in harmonics is correlated. Population statistics generally not gaussian. Olber's paradox for Gravitational Radiation Given some local bright gravitational radiation source, why isn't the rms strain from all cosmological sources divergent? h ~ 1/d , N proportional to d , < h > ~ d

L L 3 L 1⁄2

NB: L

• f course has same ``problem'' as classic Olber's paradox.

GW Footnote: Flanagan noted that strictly the GW ``Olber's paradox'' is the same as for electromagnetic radiation, as per the NB above. In practise it is a bit worse for GW than E&M, because of the combined effects of cosmology, cosmological evolution of sources, and redshifting of emitted frequency at high redshift to locally observed frequency - this makes the contribution from ``the edge of the universe'' a little bit more dominant than expected from strict 1/r Ļ r contribution canceling out.

2 2

Silly: universe has finite age - therefore finite number of sources.

Aside: If universe were decelerating, <h> would be increasing with time as horizon volume became larger. Accelerating universe, won't happen - <h> -> 0. Curious.

So we can integrate over all sources, scaled to some local population density, and correct for evolution. h (f) = 3Ļ 10 ( ) (f/10 Hz) (N Mpc ) F(z)

c

• 24

M 5/6

• 3
• 2/3
• 3 1⁄2

From Phinney (2001a) Have to be a little bit careful - local universe is not homogenous.

Aside: SN rate is 10 y in our galaxy. So global rate is few per second. Each produces ~0.1 s burst (modulo (1+z) effects). So near continuous bursts.

• 2
• 1

One in billion is thousand times closer than average, may be seen by LIGO if all goes well. To get inside local group, can't use average, LIGO would need to operate for 100 years to rely on local statistics.

Extragalactic background not a problem for LIGO.

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Have 10 mergers == 1 per year. h ~ 10 ! This is because LIGO can only barely see the foreground. If we see ``local'' single source (d ~ 10 kpc), then the 10 similar sources out at 1 Gpc, will contribute at comparable level!

L 10

LISA has galaxy dominate foreground because nearest compact binary is very close. Extragalactic background at ~ 30% level. Using GAIA/SIM to find nearest and brightest compact binaries, doing spectroscopy (mid/high res spectroscopy of 10 -10 candidates from 10 or more stars!) will allow us to fit maybe 1/3 of ``right shoulder'' of the LISA foreground.

5 7 10

Then rest is irreducable and about equal galactic and extragalactic. What about SMBH? We have N ~ 10 for ~ 10 M SMBH.

• 3

6 sun

Assume merger. ~ 10 for major mergers. One per object. M

6 10 c

• 19

Merger takes about one year. No confusion. So what is the problem... Consider high mass ratio mergers in LISA waveband:

• h ~ 10

N , but now each SMBH may have undergone 10 mergers over all z - so we expect <h> ~ 10

• due to multiple events dawdling in LISA waveband.

c

• 23

1⁄2 4

• 21

Nearest event at any one time is ~20 times closer than mean distance, so has h ~ 10 , separates from noise.

max

• 19.5

Correlated noise, non-gaussian. Small number of contributing events, coarse frequency bins and harmonics have correlated power due to high eccentricity. Interesting question - can we do better in different waveband? Expect we can - because we picked LISA waveband to be where foreground sources are, which necessarily therefore has high background!

So what about cosmology?

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``Standard model'' - Omega h <~ 10 , flat spectrum.

2

• 14

anchored by CMB, so normalised at low frequency end. Need LISA II to detect, maybe. Boring. Alternative scenarios: tilt spectrum

• tilt down, even less power in GW observatory bands
• tilt up (eg ekpyrotic universe) - could come up into LIGO band! Hard to arrange for interesting tilt without

violating existing bounds.

• new physics at 10 TeV (LED) or 10 GeV (GUT) - broken spectrum, strong peak in LISA or LIGO
• peak. Needs more calculation, long shot.

10

Assuming no radical new physics (and how would we know if we did see radical new cosmological physics?), then we need to push hard in some waveband and look for one with low ``foreground''. And do Sagnac calibration, cross-correlation if n>1 observatories.

So, where do we want to go tomorrow?

Do we want to go to MAGGIE - intermediate frequency? Or to ultra-low frequency with Large LISA II? Do we work more on improving h (beyond ``normal'' improvements in optics, laser power etc)?

min

Or do we work on flying multiple observatories for cross-correlation and coincidence? YES. What is the astrophysical foreground at microHz? Want to get to ~ 10 at microHz or so for cosmology.

• 20

Domain of >~ 10 M SMBH mergers - equal mass and high mass ratio.

8 sun

• There are maybe only ~ 10

SMBH with that high a mass.

7.5 ± 0.5

We expect only ~30% to have undergone major mergers. Takes ~10 years to go through microHz range. So at any one time, there are only few in process of merger.

3

Having 10 M SMBH doesn't help, mass function steep, only add ~ 10% to rate even if each undergoes multiple major mergers.

9 sun

2/21/02 9:25 AM GWPW'01 talk Page 5 of 7 http://www.astro.psu.edu/users/steinn/gwpw.html

So what about high mass ratio mergers? h ~ 3Ļ 10 N .

c

• 23

1⁄2

These are in lower density stellar environments - current merger rate is ~10 y

• r less. So default N ~

10 . So not a problem.

• 8
• 1
• 2

How bad can it get? If each SMBH scours the ``excess stellar population'', then there maybe ~10 high mass ratio mergers per SMBH. We'll use 10 to be conservative. Then N <~ 10 Mpc at worst.

5 6 3

• 3

Still not a problem. Gets to be a problem only at higher frequencies. Stops being a problem again as you go above LISA waveband, because there are probably no sources spending any time in that waveband, unless IMBHs do a lot of coalescing at high redshift, in which case that waveband is closed (due to confusion by high z background), but we should see this in LISA as well. So what should we do? ``Practice random kindness and senseless acts of beauty''

LIGO is a facility. LISA is a mission.

We need to start thinking in terms of an ongoing space based gravitational wave observatory, that receives

• upgrades. Not new missions.

Ideally we replace detectors in LISA, with normal improved detectors, preferably with overlap with first LISA to get simultaneous coverage. This is assuming we are right and LISA sees interesting stuff. Then we need to use LISA data to decide where to step next: higher or lower in f? with two identical detector sets? with heterogenous detectors sets? where is diminishing return in integrating longer? How will we recognise the cosmic background when we see it, and will we care by then? Footnote: per Stebbins' request, I would recommend, given current knowledge, that we should go to higher frequencies for LISA II. That is, the next mission should go into the ``frequency gap'' between LISA and LIGO (MAGGIE concept type mission). Such a mission should, of course, push the strain sensitivity limit as far as practicable, but idealy should fly in time to overlap with LISA's operational lifetime, and have bandwidth overlapping the LISA band in order to take advantage of the opportunity to cross-correlate signals.

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This is assuming that LISA detects high S/N point source signals from SMBH mergers, and is not severly confusion limited from high z background at all frequencies. If no high S/N signals are seen with LISA, then it may be better to go to lower frequencies initially in the hope of seeing SMBH coalescence there, though the expected rate of observable events at low frequencies, given no LISA signal, would have to be thought about long and hard. The standard model primordial background is probably easier to see at lower frequencies, but the prospects for ``new physics'' cosmological signals are better at higher frequencies, and there is the prospect of seeing IMBH coalescences from Pop III and formation of SMBHs at the higher frequencies. Then LISA III might be a ultra-low frequency detector, preferably a pair of detectors to get cross-

• correlation. Obviously by this stage the science would be driven by what LISA has already
• bserved, or failed to observe.

Getting there isn't half the fun - it's all the fun

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