Galactic binary foregrounds Resolving, identifying and subtracting binary stars Shane L. Larson Space Radiation Laboratory California Institute of Technology shane@srl.caltech.edu Pennsylvania State University State College, PA 18 October 2003
STORYLINE LISA, binary star foregrounds and modulations gclean method & examples» Cornish & Larson Summary» Outstanding issues
Galactic binary foregrounds Estimates suggest ~10 7 close binaries in galaxy visible in gravitational waves So many that at low frequencies, the GW signal merges in a confusion foreground Should be ~5000 to 10,000 individually resolvable to LISA Bender & Hils (1997) Nelemans, Yungelson, Portegies Zwart (2001)
10-20 Classic estimate by Bender/Hils h 10 10-21 -22 Fall off at ~2 mhz is where can "see through" the confusion Diamonds are the -23 10 6 closest, well studied binaries (AM CVn's) -- -24 10 the "LISA guaranteed sources" -25 10 0.0001 0.001 0.01 0.1 f [Hz]
10 Realization by Phinney -20 No AM CVn's, realistic galaxy model, kludged chirp mass distribution h 10-21 10-22 10-23 Net result: missing low amplitude sources at high frequency 10-24 10-25 0.0001 0.001 f [Hz] 0.01 0.1
The Subtraction Question Natural question to ask -- can we get rid of these? Can we resolve single binaries? Goal to see different signals: individual binaries, EMR captures, SMBH mergers... Signals can easily be buried in foreground How can we "subtract" binaries? How well can we do the subtraction?
Keep in mind... There is information here! These aren't just noise (contrary to popular opinion)! binary physics binary distributions Subtraction methods naturally point toward astrophysical parameters of these systems There will be an ultimate confusion limit Shannon's Theorem (limited by SNR) "Helling's 3 bin rule"
Ultimate confusion limit will set sensitivity, merged foreground + instrumental noise 10-18 10-19 10-20 h 10-21 10-22 10-23 10-24 10-5 0.0001 0.001 0.01 0.1 1 f [Hz]
Binary Signals in LISA data To subtract, need to recognize signal in data Binaries are "monochromatic", but problem of identification is exacerbated by LISA
Modulations in LISA data Three distinct modulations we can characterize FM (Doppler) due to relative motion AM due to sweep of antenna pattern on sky PM due to varying sensitivity to polarization 1.5 AM 0.12 0.1 FM 1.0 0.08 0.06 0.5 0.04 0.02 0 0.009999 0.01 0.010 0 0.009999 0.01 0.010 0.6 PM 0.06 TM 0.4 0.04 0.2 0.02 0 0.009999 0.01 0.010 0 0.009999 0.01 0.010
Identification & Subtraction Methods Identification and subtraction are linked Doppler demodulation uses LISA model to "reassemble power" for specific direction Hellings (2003), Cornish & Larson (2003) Krolak & Tinto (2003) use Doppler demodulation with maximum likelyhood estimators to determine parameters gclean iteratively subtracts small bits
CLEAN Algorithm (Hogbom, 1975) CLEAN is a method from EM image processing Identify brightest source in data Using model of instrument response, subtract small bit of signal, centered on bright source Remember where and how much subtracted Iterate first 3 steps to some prescribed level From stored record of subtractions, rebuild individual sources
gclean: CLEAN for LISA The response of LISA to a source depends on the sky location! Template matching; templates on HEALpix centers f, q, f, i, y, fo Do a coarse search, then hierarchical refinement when bright pixel found
Subtraction & Reconstruction CLEAN is a 2 step process: STEP1: identify, and subtract small bits STEP2: from small bits, rebuild source During subtraction, many templates will be used to CLEAN the spectrum Reconstruction resums subtracted bits, grouping templates which are "nearby"
Example: 1 Source 0.2 Input stream Reconstructed Residuals 0.15 Power 0.1 0.05 0 4.9996 4.9998 5 5.0002 5.0004 5.0006 5.0008 5.001 f (mhz)
Example: 1 Source 0.02 Residuals Noise 0.015 Power 0.01 0.005 0 4.999 4.9995 5 5.0005 5.001 f (mhz)
Example: 1 Source, Parameters Can compare the parameters I input to the recovered parameters from reconstruction Input Recovered q 0.79 0.79 f 2.21 2.21 i 2.45 2.11 y 1.62 1.63 fo 0.71 0.81
Example: 3 Sources 0.4 0.35 0.3 0.25 Power 0.2 0.15 0.1 0.05 0 4.999 4.9995 5 5.0005 5.001 f (mhz)
Example: 3 Sources 0.25 0.2 0.15 Power 0.15 0.1 0.05 Power 0.1 0.05 0 0-0.05 4.999 4.9992 4.9994 4.9996 4.9998 5 5.0002 5.0004 f (mhz) 0.12-0.05 4.999 4.9995 5 5.0005 5.001 f (mhz) 0.1 0.08 Power 0.06 0.04 0.02 0-0.02 4.999 4.9995 5 5.0005 5.001 f (mhz)
Example: 3 Source, Parameters Can compare the parameters I input to the recovered parameters from reconstruction q 0.66 0.67 2.87 2.85 1.40 1.50 f 3.32 3.33 0.26 0.42 4.35 4.37 i 2.86 1.98 2.64 1.79 1.57 1.57 y 1.42 1.10 0.26 0.44 1.10 1.04 fo 1.84 1.22 2.00 1.10 1.18 1.49 Additionally, there are several spurious sources with amplitudes about 1/3 of these
Summary Binary foregrounds will be prominent in LISA data Methods like gclean can identify and subtract Will subtract anything out of the data! For just a few sources, computationally intensive Generates large number of spurious sources Unanswered questions What are ultimate limits? Can we approach the information theory bounds? How will work with LOTS of sources? Different sources? Other methods?