24 Jan 2006. Dear all, Here is a proposed preliminary recommendation for input to the ESA Astrium studies of 5Gm vs 2Gm arms for LISA, based on the data in Sterl's hands as of 11pm PST, Jan 24 2006 (from Ryan Lang & Scott Hughes & Sterl Phinney). They are preliminary in the sense that: i) there is not yet simulated data for 4,7,14 days before merger for all (z,M1,q) cases of interest. ii) corrections have not yet been applied for non-circular sky error ellipses, for LISA's variable sky sensitivity, or for the failure of the Fisher matrix estimates at high parameter number and modest SNR, or for systematic errors introduced by template mismatch. All of these will make things worse for all the LISA configurations, and make the requirements even more stringent. iii) the recommendation has not been voted/vetted by the full LIST or WG1, though parts of it have been by subsets of the LIST. In the convention where standard pre-phase A LISA has single-link position noise of 20pm/rtHz: * 2Gm arm length with single-link position noise worse than 15pm/rtHz would significantly impact LISA science requirements for A) supermassive black holes, B) the search for < 10^5 Msun black holes at z>5, and C) extreme-mass ratio inspiral tests of black holes and GR. *** Thus 2Gm arm with single-link position noise worse than 15pm/rtHz is not likely to prove scientifically acceptable for a baseline mission. * 2Gm arm length with single-link position noise better than 9pm/rtHz would only significantly impact the (highest priority) LISA science requirement for A) Supermassive black holes, as follows: i) 75% sky position errors for 1e7/3e6 Msun BH mergers at z=1 (`guaranteed mergers', expect a few in 3 year mission) a week before merger are larger than the 5-7 degree fields of LSST and other wide field telescopes with the sensitivity required to seek electromagnetic counterparts of the GW sources. ii) The 75% comoving volume uncertainty in the gw-determined source location after the merger is some 10-30 times larger than for 5Gm arms, making post-merger identification of host galaxies unlikely for any BH mergers at z=1-5, except for 3e5/1e5Msun BH mergers at z=1 (model dependent rate of ~ 1 in 3 years, not guaranteed). iii) Provided most black holes are spinning with a/M>0.3, the final 75% confidence fractional errors in the estimated luminosity distance are good enough (<0.1) that one could infer useful merger rates as a function of (z,M1,q) even without electromagnetic counterparts. However, if most black holes are not spinning, this science begins to be impacted. *** Thus 2Gm arm with single-link position noise better than 9pm/rtHz might be scientifically acceptable for a baseline mission, if a substantial cost saving justified the science losses compared to the 5Gm baseline. Sterl Sources of input: Choice of "reasonable" position noises for 2Gm arms: http://www.its.caltech.edu/~esp/lisa/lisa2Gmrec.txt Plots of those noise curves, without http://www.its.caltech.edu/~esp/lisa/lisa2Gmrec.pdf and WITH galactic & extragalactic white dwarf binary noise after best-case fitting: http://www.its.caltech.edu/~esp/lisa/lisa2Gmrecwd.pdf Precision of position/distance estimates for Monte Carlo simulations of LISA detection of spinning SMBH mergers, including amplitude modulation: raw data: http://gmunu.mit.edu/LIST/summary.html somewhat digested data: http://www.its.caltech.edu/~esp/lisa/armlengthrecJan23.txt This document: http://www.its.caltech.edu/~esp/lisa/armlengthrecJan24.txt LISA science requirements: http://www.its.caltech.edu/~esp/lisa/SRDwg_dec05.pdf