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Richard O’Shaughnessy U. Chicago, KICP Feb 23, 2007
Astrophysical constraints on BH-NS and NS-NS mergers and the short GRB redshift distribution I’m here to tell you + how often we think compact binaries merge (next slide) Richard O’Shaughnessy U. Chicago, KICP Feb 23, 2007 LIGO-G Z
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Outline Gravitational Wave Searches for Binaries
How to Make Compact Binaries Population synthesis Predictions and Constraints: Milky Way Comparing predictions to observations Physics behind comparisons : what we learn What if a detection? Why Ellipticals Matter Two-component star formation model Predictions and Constraints Revisited Prior predictions Reproducing Milky Way constraints Short GRBs Conclusions + about our parameterized models for how stars form from gas, evolve as binary stars, supernovae, and eventually end up (or not) as compact binaries, + how we test that understanding against the milky way, to calibrate our understanding of the evolution of the most massive binary stars + how we extend our understanding to a realistic heterogeneous universe, consisting of both old and young stellar populations, + what our best understanding of a heterogeneous universe leads us to expect for short GRBs, if indeed short GRBs arise from merging binaries, + and whether that understanding agrees with short GRB observations, whether when we combine our understanding of binary evolution with a heterogeneous universe we can explain observations of short GRBs in terms of mergers of compact objects. I’m also here to talk about gravitational wave astronomy, because -- as I hope I’ll demonstrate -- I think gravitational waves are + the best way to improve our understanding of binary mergers and + the *only* way (short term) to unambiguously investigate the central engines of short GRBs and test the merger hypothesis LIGO-G Z
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Collaborators V. Kalogera Northwestern C. Kim Cornell
K. Belczynski New Mexico State/Los Alamos T. Fragos Northwestern J. Kaplan Northwestern LSC (official LIGO results) Of course, this project isn’t my work alone… LIGO-G Z
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Big Picture Gravitational Waves EM Waves Source: Weak coupling:
~ any accelerating matter Weak coupling: Imaging impractical: (strong sources) <~ wavelength Hard to make & detect Hard to obscure Source: ~any accelerating charge s Strong coupling: Imaging often practical: (common sources) >> wavelength Easy to make & detect Easy to obscure I’m interested in compact binaries primarily because of the gravitational waves they emit during their last few minutes to seconds before they merge. Point: Gravitational waves introduced, by analogy to EM waves Text: Gravitational waves are very similar to EM waves. +For example, they are both in some sense a consequence of causality: electromagnetic waves tell distant charges that some charge has moved; gravitational waves…mass has moved. So just about any accelerating matter distribution produces waves +Physically no useful “large sources” composed of many small emitters (such as the sun, the earth, etc)…not because they don’t *exist* (I am making by waving my hands), but because their waves are too hard to detect! +Gravity, recall, is the weakest of all forces (otherwise crushed) *** NEED NUMBER *** So gravitational waves are much weaker than their electromagnetic counterpart: hard to make, hard to detect. However, that also means they aren’t *absorbed* by intervening matter --- slide break to image [This property is important: in astronomy, all too often interesting processes are obscured by intervening dust; here I show an example of star forming regions, highly dusty regions in which young stars are being born.] LIGO-G Z
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Big Picture: Spectrum Big bang Sources Detectors Supernovae
LISA (planned) LIGO (running) Sources Detectors (m) f(Hz) Pulsar timing CMB fluctuations Big bang 10-8 1016 10-6 Merging Black Holes: Big (center of galaxy) Small (post-supernova) Space-based interferometers (LISA) 10-4 1012 10-2 1010 Point: - just as in EM, different scales of radiation couple differently to matter, and are therefore 1) produced by different sorts of sources and 2) require different types of detectors to probe them 1 108 Supernovae Ground-based interferometers (LIGO/VIRGO/GEO/TAMA) 102 106 Spinning neutron stars 104 104 …and more! LIGO-G Z
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Big Science Payoff …and much more Test GR (in detail) Cosmology
Orbits agree EMRI mergers Spacetime agrees EMRI mergers Cosmology Trace galaxy mergers? Binary mergers Waves from inflation? Stochastic Nuclear physics Compressibility of NS disruption nuclear matter NS surface bumps Supernovae Constrain asymmetry Supernovae bursts and kick Binary mergers Spin imparted? Binary mergers Stars near galaxy centers Capture rates Small compact binaries Map all faint, close (“white dwarf”) binaries Mass transfer, tidal coupling, Understand stellar evolution Mass transfer rates Binary mergers Maximum NS mass Binary mergers Reveal mystery : GRB engines: Hypermassive NS? Merger-driven? Because these waves pass through everything and are emitted from the most energetic events in the universe, gravitational wave astronomy has an enormous payoff that shouldn’t be underestimated. For example, just for the case of BH-NS inspiral, we can test - properties of one merger : Nuclear matter: since the NS will disrupt during the last stages of inspiral … Look inside central engine of explosions, such as SN or (more pertinent here) GRBs. - statistics of many mergers: Formation channels : … this is the subject of this talk …and much more LIGO-G Z
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Small effect at earth! Example: Characteristic relative length changes
Two black holes Newtonian circular orbit Characteristic relative length changes ~ (kinetic energy)/(distance) r d Sensitivity needed? (LIGO) L ~ h L ~ km ~ 4 x cm laser light ~ 10-4cm atom ~ 10-8cm proton ~ 10-13cm At heart, however, all this depends on our ability to measure very, very small changes. How small? Well, to order of magnitude, a gravitational wave produces a relative legnth change of order ‘h’, for h the ratio of (kinetic) to (distance) LIGO-G Z
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Sensitivities of detectors
Present sensitivities: LIGO Reached ~ design sensitivity This small length change requires very delicate experiments. Still the sensitivities needed have been reached, both by the US program (LIGO) LIGO: at target taking data (~2 calendar yr) LIGO sensitivity page LIGO-G Z
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Sensitivities of detectors
Present sensitivities: Others GEO at target much less sensitive Point: Not just one detector, but a global network …and by a European detector. VIRGO near target target: noise < LIGO at low, high f Valiente, GWDAW-11 LIGO-G Z
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Sensitivities of detectors
Lots of astrophysically relevant data: Example: Average distance to which 1.4 MO NS-NS inspiral range (S/N=8) visible Plot from Patrick Brady’s talk Marx, Texas symposium LIGO-G Z
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Sensitivities of detectors
Range depends on mass For Mo binaries, ~ 200 MWEG (# of stars <-> our galaxy) in range For 5-5 Mo binaries, ~ 1000 MWEGs in range Plot: Inspiral horizon for equal mass binaries vs. total mass (horizon=range at peak of antenna pattern; ~2.3 x antenna pattern average) …using only the ‘inspiral signal’ (=understood) no merger waves no tidal disruption influences Plot from Patrick Brady’s talk LIGO-G Z
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Gravitational plane waves
Stretching and squeezing Perpendicular to propagation Two spin-2 (tensor) polarizations L LIGO-G Z
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Detecting gravitational waves
Interferometer: Compares two distances Sensitive to [tunable] Each interferometer = (weakly) directional antenna L-L L+L Jay Marx, Texas symposium 2006 LIGO-G Z
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Measuring inspiral sources
Using only ‘inspiral’ phase [avoid tides, disruption!] Mass Must match! df/dt -> mass Distance Location on sky Orbit orientation (Black hole) spin Precession Only if extreme Sample uses: short GRBs 1) Easily distinguish certain short GRB engines: ‘High’ mass BH-NS merger NS-NS merger 2) Host redshifts w/o afterglow association Polarized emission …and some prospect to do better for (1) -- see recent Janka paper for example on BH-NS mergers, Spin-orbit coupling LIGO-G Z
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Interpretation Challenge
“We saw three binary mergers…now what?” Preparing to interpret measurements (detections and upper limits) sometimes many are needed Statistics of detection: If we detect several binary mergers we need to know how likely we are to see this many: How many binary stars are in range? [Galaxy catalogs, normalization] What formation channels could produce mergers this often? What channels could produce these specific mergers? better than 30%?? Point: Without coincident EM measurements, interpreting a single event is difficult…we need *statistics*, to determine impact of result. …most of this talk LIGO-G Z
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Activity: Models and Analysis
Inner product: Input signal (fourier transform) Model (“template”) Sensitivity Models Necessary: Detection hard to find small signal in noise Interpretation Understand detected signal Matched filtering Kip, p 30 LIGO-G Z
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Outline Gravitational Wave Searches for Binaries
How to Make Compact Binaries Evolution of gas to merger Observable phases Population synthesis and StarTrack Predictions and Constraints: Milky Way Why Ellipticals Matter Predictions and Constraints Revisited GRBs Conclusions LIGO-G Z
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Prototype Text area (figures to right) Reference (to me)
LIGO-G Z
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Observed pulsar binaries
Hulse-Taylor binary: (Nobel Prize, 1993) PSR B Weisberg & Taylor 03 Reference (to me) LIGO-G Z
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Binary stellar evolution
Complex process Outline of (typical) evolution: Evolve and expand Mass transfer (perhaps) Supernovae #1 Supernovae #2 Note Massive stars evolve faster Most massive stars supernova, form BHs/NSs Mass transfer changes evolutionary path of star Movie: John Rowe LIGO-G Z
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Binary stellar evolution
Parameterized (phenomenological) model Example: Supernovae kicks Neutron stars = supernovae remnants Observed moving rapidly : Supernovae asymmetry --> kick Model: “Two-temperature thermal” distribution Many parameters (like this) change results by x10 Hobbs et al Observations suggest preferred values conservatively: explore plausible range LIGO-G Z
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StarTrack and Population Synthesis
Evolve representative sample See what happens Variety of results Depending on parameters used… Range of number of binaries per input mass Priors matter a priori assumptions about what parameters likely influence expectations Plot: Distribution of mass efficiencies seen in simulations More binaries/mass O’Shaughnessy et al (in prep) LIGO-G Z
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StarTrack and Population Synthesis
Evolve representative sample See what happens Variety of results Depending on parameters used… Range of number of binaries per input mass Range of delays between birth and merger Priors matter a priori assumptions about what parameters likely influence expectations Specifically: Popsyn case: Uniform priors GRB case Priors are the set of *simulated* systems…which because of irregular v sampling don’t agree with *either* the first paper (which used the truncated region v2>200>v1) or the second (which uses the whole region, uniformly) Plot: Probability that a random binary merges before time ‘t’, for each model Merging after 2nd supernova Merging after 10 Gyr O’Shaughnessy et al (in prep) : changed priors since last paper LIGO-G Z
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Outline Gravitational Wave Searches for Binaries
How to Make Compact Binaries Predictions and Constraints: Milky Way Observations (pulsars in binaries) and selection effects Prior predictions versus observations Constrained parameters Physics behind comparisons : what we learn Revised rate predictions What if a detection? Why Ellipticals Matter Predictions and Constraints Revisited GRBs Impact of detection(s)? Conclusions LIGO-G Z
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Observations of Binary Pulsars
7 NS-NS binaries 4 WD-NS binaries Selection effects “How many similar binaries exist, given we see one?” Examples Lifetime : age + merger time < age of universe Lifetime visible : time to pulsar spindown, stop? Fraction missed - luminosity: many faint pulsars Distribution of luminosities ~ known Fraction missed - beaming: Not all pointing at us! Kim et al ApJ (2003) Kim et al astro-ph/ Kim et al ASPC (2005) Kim et al ApJ (2004) Rate estimate Kim et al ApJ (2003) (steady-state approximation) Number + ‘lifetime visible’ + lifetime + fraction missed => birthrate + error estimate (number-> sampling error) Note: Only possible because many single pulsars seen: Lots of knowledge gained on selection effects Applied to reconstruct Ntrue from Nseen Example: Lmin correction: One seen --> many missed LIGO-G Z
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Predictions and Observations
Formation rate distributions Observation: shaded Theory: dotted curve Systematics : dark shaded Allowed models? Not all parameters reproduce observations of NS-NS binaries NS-WD binaries (massive WD) --> potential constraint Plot Merging (top), wide (bottom) NS-NS binaries LIGO-G Z
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Accepted models Constraint-satisfying volume 9% of models work 7d grid
7d volume: Hard to visualize! Extends over ‘large’ range: characteristic extent(each parameter): 0.091/7~0.71 9% of models work 7d grid = 7 inputs to StarTrack LIGO-G Z
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Accepted models Parameter distributions
Not all parameter combinations allowed Examples: Kick strength: v1,v2~ 300 km/s CE efficiency: >0.1 Mass loss : fa<0.9 Lots of physics in correlations LIGO-G Z
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Physics of comparison Physics implied by constraints
Kick strength: v1,v2~ 300 km/s Pulsar motions ~ measure supernova kicks [e.g., Hobbs 2006] Preferred kicks ~ consistent with observations (without imposing that as a constraint) LIGO-G Z
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Physics of comparison Physics implied by constraints
CE efficiency: >0.1 CE efficiency = fraction of orbit energy needed to eject envelope surrounding two cores Low : closer final orbit needed to eject envelope some binaries merge in CE phase! - NS-NS rate down - BH-NS rate up (often) - BH-BH rate up brings together distant holes Excluding low: High NS-NS rate needed to match observations Low can’t make it Posterior rate prediction: lower BH-BH rate Plot: BH-BH merger rate versus ; low imply high rate LIGO-G Z
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Revised rate predictions
Rate predictions change… Solid: Prior Dashed: After constraint Warning: Priors matter Exact mean, probabilities depend on priors/assumptions (= range of parameters allowed) Trend of change (before vs after) rather than specifics Fewer BH-BH More NS-NS (of course) LIGO-G Z
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LIGO detection rates Constrained LIGO detection rates
Assume all galaxies like Milky Way, density 0.01 Mpc-3 Key NS-NS BH-NS BH-BH Detection unlikely Detection assured LIGO-G Z
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Detection: A scenario for 2014
Scenario: (Advanced LIGO) Observe n ~ 30 BH-NS events [reasonable] Rate known to within d log R ~1/n1/2ln(10)~ 0.08 Relative uncertainty down by factor d log R/ log R ~ 0.08/1 8% < 9% : More information than all EM observations (used) so far! Repeat for BH-BH, NS-NS Independent channels (each depends differently on model params)-> Volume [0.09 (0.08)3] ~ (4 x 10-5) !! Params [0.09 (0.08)3]1/7 ~ 0.24 Potential Stringent test of binary evolution model already! Stronger if Orbit distribution consistency More constraints LIGO-G Z
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Outline Gravitational Wave Searches for Binaries
How to Make Compact Binaries Predictions and Constraints: Milky Way Why Ellipticals Matter Two-component star formation model Predictions and Constraints Revisited Prior predictions Reproducing Milky Way constraints GRBs Conclusions LIGO-G Z
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Importance of early SFR
Long delays allow mergers in ellipticals now Merger rate from starburst: R ~ dN/dt~1/t SFR higher in past: Result: Many mergers now occur in ancient binaries ancient SFR = ellipticals (mergers, …) From recent Plot: Birth time for present-day mergers Nagamine et al astro-ph/ \ From old LIGO-G Z
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Two-component SFR SFR Separate elliptical, spiral! Reliable?
[Nagamine et al 2006] Separate elliptical, spiral! Reliable? Normalization ok Spiral/elliptical ratio ok Time dependence reasonable …uncertainty smaller than popsyn Nagamine et al astro-ph/ LIGO-G Z
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Predictions and constraints
Two-component predictions: Each prediction = Rate density (/vol/time) versus time for each of ellipticals, spirals …mostly unobservable (except now in Milky Way) Example: NS-NS merger rate in spirals Rate extrapolated from Milky way: Rs= Myr-1Mpc-3 assuming a spiral galaxy density 0.01 Mpc-3 consistent parameters unfinished / pending revised merger & LIGO rates discuss in context of short GRBs LIGO-G Z
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Outline Gravitational Wave Searches for Binaries
How to Make Compact Binaries Predictions and Constraints: Milky Way Why Ellipticals Matter Predictions and Constraints Revisited GRBs Review + the short GRB merger model Short GRB observations, the long-delay mystery, and selection effects Detection rates versus Lmin Predictions versus observations: If short GRB = BH-NS If short GRB = NS-NS Gravitational waves? Conclusions LIGO-G Z
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Short GRBs: A Review Short GRBs (BATSE view) Cosmological
One of two classes Hard: often peaks out of band Flux power law dP/dL ~ L-2 --> most (probably) unseen Many sources at limit of detector (BATSE) Reference (to me) LIGO-G Z
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Short GRBs: A Review Merger motivation? No SN structure in afterglow
In both old, young galaxies Occasional host offsets GRB (Fox et al Nature ) GRB (Soderberg et al 2006) Energetics prohibit magnetar LIGO-G Z
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Observables: Detection rate?
Short GRBs Few observations Minimum luminosity ~ unknown Observed number --> rate upper bound Binary pulsars Many (isolated) observed Minimum luminosity ~ known Observed number --> rate (+ ‘small’ error) Plots: Cartoon on Lmin observed Conclusion: The number (rate) of short GRB observations is a weak constraint on models LIGO-G Z
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Observables: Redshift distribution
Redshift distribution desirable Low bias from luminosity distribution Well-defined statistical comparisons Kolmogorov-Smirnov test (=use maximum difference) Observed redshift sample Need sample with consistent selection effects (=bursts from , with Swift) Problem: Possible/likely bias towards low redshifts LIGO-G Z
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Merger predictions <-> short GRBs?
BH-NS?: Predictions: 500 pairs of simulations Range of redshift distributions Observations: Solid: certain Shaded: possible Key Solid: % Dashed: 10-90% Dotted: 1%-99% O’Shaughnessy et al (in prep) LIGO-G Z
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Merger predictions <-> short GRBs?
BH-NS?: Predictions that agree? Compare cumulative distributions: maximum difference < 0.48 everywhere Compare to well-known GRB redshifts since 2005 dominated by low redshift [95% Komogorov-Smirnov given GRBs] [consistent selection effects] Result: Distributions which agree = mostly at low redshift O’Shaughnessy et al (in prep) LIGO-G Z
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Merger predictions <-> short GRBs?
BH-NS?: Physical interpretation Observations : Dominated by recent events Expect: Most mergers occur in spirals (=recent SFR) and High rate (per unit mass) forming in spirals or Most mergers occur in ellipticals (=old SFR) and High rate (per unit mass) forming in elliptical and Extremely prolonged delay between formation and merger (RARE) Mostly in ellipticals Plot: fs : fraction of mergers in spirals (z=0) Mostly in spirals Consistent…but… Short GRBs appear in ellipticals! BH-NS hard to reconcile with GRBs?? O’Shaughnessy et al (in prep) LIGO-G Z
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Merger predictions <-> short GRBs?
BH-NS?: Conclusion = confusion Theory + redshifts : Bias towards recent times, spiral galaxies Hosts: Bias towards elliptical galaxies What if observations are biased to low redshift? strong indications from deep afterglow searches [Berger et al, astro-ph/ ] Makes fitting easier Elliptical-dominant solutions ok then (=agree w/ hosts) Point: Too early to say waiting for data; more analysis needed LIGO-G Z
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Merger predictions <-> short GRBs?
Key Solid: % Dashed: 10-90% Dotted: 1%-99% NS-NS?: Predictions & observations Matching redshifts Observed NS-NS (Milky Way) All agree? - difficult O’Shaughnessy et al (in prep) LIGO-G Z
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Merger predictions <-> short GRBs?
NS-NS?: Physical interpretation Observations : GRBs Dominated by recent events Expect: Recent spirals dominate or or Ellipticals dominate, with long delays -Observations: Galactic NS-NS High merger rate Expect High merger rate in spirals Solid: Unconstrained Dashed: Dotted: Plot: fs : fraction of mergers in spirals (z=0) Consistent…but… Short GRBs appear in ellipticals! NS-NS hard to reconcile with GRBs and problem worse if redshifts are biased low! Mostly in ellipticals O’Shaughnessy et al (in prep) Mostly in spirals LIGO-G Z
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Detection: When, and what? (*)
REVISED LIGO DETECTION RATES? Correlation with GRB? Reference (to me) LIGO-G Z
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Prototype Text area (figures to right) Reference (to me)
LIGO-G Z
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Conclusions Present: (Long term) Wishes formation history
Useful comparison method despite large uncertainties Preliminary results Via comparing to pulsar binaries in Milky Way? Low mass transfer efficiencies forbidden Supernovae kicks ~ pulsar proper motions BH-NS rate closely tied to min NS mass/CE phase [Belczynski et al in prep] Via comparing to short GRBs? Conventional popsyn works : weak constraints-> standard model ok Expect GRBs in either host : spirals form stars now Spirals now favored; may change with new redshifts! Short GRBs = NS-NS? hard : few consistent ellipticals Short GRBs = BH-NS? easier : fewer observations Observational recommendations Galactic : Minimum pulsar luminosity & updated selection-effect study Pulsar opening angles Model : Size and SFR history Short GRBs : Ratio of spiral to elliptical hosts at z<0.5 (Long term) Wishes (critical) reliable GRB classification short burst selection bias? deep afterglow searches (less critical) formation history formation properties (Z, imf) [mean+statistics] for all star-forming structures Point for preliminary: MW: Lots of observations, so very hard questions can be asked now Universe: Fewer constraints outside of the milky way, so it’s harder to ask questions and constrain with very high confidence. LIGO-G Z
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Belczynski et al. (in prep)
Conclusions Future (model) directions: More comparisons Milky Way Pulsar masses Binary parameters (orbits!) Supernova kick consistency? Extragalactic Supernova rates Some examples: Belczynski et al. (in prep) Broader model space Polar kicks? Different maximum NS mass [important: BH-NS merger rate sensitive to it!] Different accretion physics Final: Early days Lots yet to be done to confirm and flesh out, but … It looks like we understand Goal: - show predictions robust to physics changes - if changes matter, understand why (and devise tests to constrain physics) LIGO-G Z
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Appendix: Timeline Timeline to inspiral detection Timeline & funding
LIGO today Advanced LIGO ~2014 Enhanced LIGO ~2009 Timeline to inspiral detection Timeline & funding LIGO / VIRGO : NSF+Europe LISA : NASA …build LISA Possible detection Good science even w/o 2007 2008 2009 2010 2011 2012 2013 2014 Detection assured Part 1: -Survey to show knowledge - to review areas in which I contribute Initial LIGO (S5) Enhanced LIGO (S6) (x2 range!) Advanced LIGO VIRGO?? VIRGO VIRGO+ Sources: LIGO : Marx, Texas Symposium (G060579)+ G060358; VIRGO: tentative -- coordination pending; Valiente GWDAW 2006 LISA: NASA Beyond Einstein review (2006) LIGO-G Z
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Appendix: LIGO searches
The following slides are for reference and not presentation! Inspiral search : Prelminary Results GRB search : Summary and results LIGO-G Z
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Inspiral search summary
S4 upper limits-compact binary coalescence Rate/year/L10 vs. binary total mass L10 = 1010 Lsun,B (1 Milky Way = 1.7 L10) Dark region excluded at 90% confidence. Preliminary 10 / yr / L10 1 / yr / L10 Mo Slide #3 (only if you want + we can get approval from review committee): rate upper limits based on the S4 searches. 0.1 / yr / L10 Msun LIGO-G Z
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Triggered Searches for GW Bursts
preliminary Triggered Searches for GW Bursts Swift/ HETE-2/ IPN/ INTEGRAL RXTE/RHESSI LIGO-LHO LIGO-LLO search LIGO data surrounding GRB trigger using cross-correlation method no GW signal found associated with GRBs in S2, S3, S4 runs set limits on GW signal amplitude 53 GRB triggers for the first five months of LIGO S5 run typical S5 sensitivity at 250 Hz: EGW ~ 0.3 Msun at 20 Mpc Gamma-Ray Bursts galactic neutron star (10-15 kpc) with intense magnetic field (~1015 G) source of record gamma-ray flare on December 27, 2004 quasi-periodic oscillations found in RHESSI and RXTE x-ray data search LIGO data for GW signal associated with quasi-periodic oscillations-- no GW signal found sensitivity: EGW ~ 10–7 to 10–8 Msun for the 92.5 Hz QPO this is the same order of magnitude as the EM energy emitted in the flare Soft Gamma Repeater
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LIGO limits on isotropic stochastic GW signal
Cross-correlate signals between 2 interferometers LIGO S1: ΩGW < 44 PRD (2004) LIGO S3: ΩGW < 8.4x10-4 PRL (2005) LIGO S4: ΩGW < 6.5x10-5 (new upper limit; accepted for publication in ApJ) Bandwidth: Hz; Initial LIGO, 1 yr data Expected sensitivity ~ 4x10-6 upper limit from Big Bang nucleosynthesis 10-5; interesting scientific territory Advanced LIGO, 1 yr data Expected Sensitivity ~1x10-9 H0 = 72 km/s/Mpc GWs neutrinos photons now Cosmic strings (?) ~10-8 Inflation prediction ~10-14 LIGO-G Z
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