Optimizing LISA for cost and science

Sean T. McWilliamsstmcwill@princeton.edu

Princeton University

LISA 9 Symposium, Paris, France

May 24, 2012

May 24, 2012 Sean T. McWilliams LISA 9 Symposium, Paris 2

Overview

• Sensitivities and rates of NGO/SGO, Omega, and GADFLI for MBHBs, EMRIs, and GBs

• MBHB parameter estimation, or why you should pay very close attention to GADFLI

• Mission details, comparisons of designs– NB: very similar concept to GADFLI, GEOGRAWI by Tinto et al

• Cost: speculative comparison

• Conclusions: GADFLI wins on MBHB science (hands down), performs on EMRIs and GBs, uses LPF heritage, and may be the cheapest option. So…

armlength (Mm) # links telescope dia. (cm) laser (W) duration (yr)# modulations

GADFLI 0.073 6 15 0.7 2 730OMEGA 1.04 6 30 1 3 7SGO/NGO 1.0 6/4 25 0.7 2 2

May 24, 2012 Sean T. McWilliams LISA 9 Symposium, Paris 3

MBHB Sensitivities and Rates

• Total SNR for GADFLI for MBHBs is less than for NGO/SGO and OMEGA

• HOWEVER, late inspiral SNR for low mass systems is largest for GADFLI

• Detection rate good for all

May 24, 2012 Sean T. McWilliams LISA 9 Symposium, Paris 4

EMRI and GB Rates

• EMRI rate a conservative variant of Gair et al., Class. Quant. Grav. 21 (2004) S1595-S1606

• Extreme uncertainty in EMRI event rates

• All options should see GBs, based on Nelemans catalog

• EMRI and GB parameter estimation generally obey

1/SNR expectations, so GADFLI should worse as N1/3, or a factor of ~4 for EMRIs, < 2 for GBs

May 24, 2012 Sean T. McWilliams LISA 9 Symposium, Paris 5

How does LISA measure MBHB parameters?

• Independent waveform channels, with different frequency and spatial dependencies (aka TDI observables)

• Frequency dependence of response function

• Intrinsic parameter dependence of waveforms (for MBHBs, q, S1, S2, e)

• Doppler modulation: annual (all) and shorter periods (geocentric)

• Intrinsic parameter dependence of waveforms (for MBHBs, q, S1, S2, e)

• Independent waveform channels, with different frequency and spatial dependencies (aka TDI observables)

• Doppler modulation: annual (all) and shorter periods (geocentric)

• Frequency dependence of response function

How to assess science performance

Waveform Model– Use a parametrized model that encodes

parameter information– Extrinsic parameters can easily be

scaled/shifted, result is robust

– Intrinsic parameters are more subtle

Instrument Modeling– Realistic orbit model

– Instrumental noises

– Full response function

May 24, 2012 6Sean T. McWilliams LISA 9 Symposium, Paris

Calculating uncertainties– Use the Fisher matrix formalism to

estimate uncertainties

– MCMC too costly, unnecessary with high SNR

(1+z)Mtot, DL, tc, φorb, θsky , θsys

q, S1 , S2, e

May 24, 2012 Sean T. McWilliams LISA 9 Symposium, Paris 7

MBHB Parameter Estimation: SGO vs. NGO

• SGO (6 links) and NGO (4 links) were compared as part of the science performance task force• Relatively poor sky localization and distance determination with NGO

May 24, 2012 Sean T. McWilliams LISA 9 Symposium, Paris 8

MBHB Parameter Estimation Without Spin

• GADFLI makes up for lost SNR with diurnal modulation – there is more (sometimes much more) to PE than SNR• HOWEVER, at December’s workshop, I said “There is good reason to believe GADFLI could outperform other designs for estimating MBHB

source parameters when spin is included, due to its sensitivity at higher frequencies, and its daily orbital modulation of signals.”…

May 24, 2012 Sean T. McWilliams LISA 9 Symposium, Paris 9

MBHB Parameter Estimation With Spin

• Spin makes a HUGE difference for parameter accuracy• Given the greater complexity in including intrinsic parameters, PE studies with spin were not completed until after the Team

X selection

courtesy of Neil Cornish

May 24, 2012 Sean T. McWilliams LISA 9 Symposium, Paris 10

MBHB Parameter Estimation With Spin

See talk by Neil Cornish tomorrow morning for more details

May 24, 2012 Sean T. McWilliams LISA 9 Symposium, Paris 11

Design comparison

• GADFLI has a far more stable orbit than SGO/NGO or Omega, mission lifetime was limited solely to decrease cost

All data provided by Gary Welter for Mission Concept Workshop

Arm variation (%)

Interior angle variation (%)

Range rate (m/s)

GADFLI 0.02 0.02 1OMEGA 0.1 12 160LISA 0.01 0.8 13

• GADFLI much less expensive for orbit insertion, does not need a propulsion module

LV C3 (km/s)2 v (m/s) Cruise duration (months)

GADFLI -9.0 1 4OMEGA -1.6 500 13LISA -0.3 1100 14• GADFLI and Omega must deal with eclipses and sunlight in the

telescope. Without mitigation, GADFLI would need to drop out of science mode for ~40 days/yr.

May 24, 2012 Sean T. McWilliams LISA 9 Symposium, Paris 12

GADFLI pros/cons

• seems to outperform even original LISA in MBHB science• no need for propulsion module• low launch mass• uses LPF GRS, space-qualified laser, highest TRL level overall• lower shot noise requirements• most stable, cheapest orbit of any conceivable option• … naively, should be less expensive than other options

• GADFLI less sensitive to EMRIs and GBs by a factor of a few

• Thermal issues must be understood

• Eclipses, sun pointing, can leave science mode in worst case

• Different face to the sun and changing Earth albedo – is thermal variability an issue?

pros

cons

Conclusions

• GADFLI measures EVERY parameter 1-2 orders of magnitude better than SGO (another 10x better than NGO for key parameters)

• sky localization of O(1 arcmin) for most sources, down to O(1 arcsec) – pinpoint individual galaxy!– These results use Cornish and Lang code, should be checked independently

• Since GADFLI has lighter/smaller components on the most stable and cheapest orbits, using as much or more LPF heritage than any other option, it should be the cheapest possibility.

• If we are “revolutionaries” and “risk-takers”, we should be willing to change our proposal if new information DRASTICALLY changes the science picture

• NB: Geostationarity and precise dimensions are NOT set in stone. Have a lot of room to increase orbit to mitigate thermal issues, make decommissioning less of an issue.

• If limitation is launch on 2 Soyez, shrink components if necessary (eg less strict shot noise req, can shrink mirror)… if budget improves, prospects with a longer mission and a fourth satellite are tantalizing

11 August 2008 13Sean T. McWilliams NRDA 2008 – Syracuse, NYMay 24, 2012 13Sean T. McWilliams LISA 9 Symposium, Paris

Questions?

11 August 2008 14Sean T. McWilliams NRDA 2008 – Syracuse, NYMay 24, 2012 14Sean T. McWilliams LISA 9 Symposium, Paris

GADFLI -- Geocentric Antenna for Drag-Free Laser Interferometry

Wikipedia defines a gadfly as “a person who upsets the status quo by posing upsetting or novel questions, or just being an irritant.” Hopefully this concept is the right balance of novel question and irritant.