Optimal search for CW directed targets

Transcription

1 Optimal search for CW directed targets Jing Ming Max Planck Institute for Gravitational Physics Albert Einstein Institute Golm and Hannover, Germany GWPAW Osaka AEI (Hannover) LIGO-G GWPAW Osaka / 26

2 Continuous Waves (CW) Continuous Wave (CW):produced by systems that have a fairly constant and well-defined frequency. AEI (Hannover) LIGO-G GWPAW Osaka 2 / 26

3 Types of CW searches Types: for known pulsars (e.g. Crab) all-sky surveys directed searches (e.g. Vela Jr, Cas A) ( the type we are dealing with) directed searches from objects with companions (e.g. Sco X-) AEI (Hannover) LIGO-G GWPAW Osaka 3 / 26

4 Basic idea CW searches are extremely computationally expensive! In the case of directed searches the sky position is known so the search parameters are : f, f and f. Our goal: Maximize the detection probability at fixed computing budget by choosing appropriately - the search set-up - the parameter space, including which targets to search In previous method: in a fixed parameter space, having chosen a specific target, tune the search set-up [K. Wette et al. 2008] and [M. Shaltev et al. 204]. AEI (Hannover) LIGO-G GWPAW Osaka 4 / 26

5 Basic procedure Basic procedure: Set computing budget Set astrophysical priors : ranges and distributions on ellipticity, f, f, f. Consider some test-set-ups (coherent segment duration, total observation time, template grids ) Consider a set of targets Use optimization scheme to determine the search set-up, parameter space on targets that maximize the detection probability constrained by the computing budget AEI (Hannover) LIGO-G GWPAW Osaka 5 / 26

6 Astrophysical prior on ε (h 0 ) Distribution of ellipticity ε: p(ε) = { ε log(ε max /ε min ) ε min < ε < ε max 0 elsewhere. () Note that: ε sd = ε sd (f, f ) ε max = min(0 4, ε sd, ε age ), ε min = 0 4. (2) Thus we have the distribution of GW amplitude h 0 : h 0 = 4π2 G c 4 I zz f 2 ε d. (3) AEI (Hannover) LIGO-G GWPAW Osaka 6 / 26

7 Astrophysical prior on f, f and f If we disregard information on the age of the targets: f : Hz, uniformly distributed f : Hz/s, uniformly distributed f : [0, nf 2 /f ]) If we fold-in the age information: f : Hz, uniformly distributed f f : [0, τ ], f : [0, nf 2 /f ] f (Hz/s) using age prior f (Hz/s) f (Hz) f (Hz) 0 AEI (Hannover) LIGO-G GWPAW Osaka 7 / 26

8 Set-ups and computing budget Detector: L and H with the same sensitivity as during S6. Duty cycle: 50%(Gaps are uniformly distributed with fixed duration) Total observation time: 300 days Coherent segment duration: 5, 0, 20, 30 days Computing power budget: 2EM (will also illustrate results for 24EM, 48EM) EM means Einstein@Home-month. EM = 2000 CPU-months. AEI (Hannover) LIGO-G GWPAW Osaka 8 / 26

9 Optimal procedure We divide the parameter space into cells, each with the same (f, f )-volume. For each cell, for each search set-up we determine : computing cost C, detection probability P and efficiency e = P/C. Constrained by computing budget, we can t search all cells. We pick cells across all targets and set-ups so that the sum of probabilites (R) over the picked cells is maximised.how do we do this? : for sources with single set-up we simply rank the cells by efficiency (ratio of probability to cost) and pick cells in order of descending rank until compute power is exhausted. 2: when considering multiple set-ups since same cells from same source with different set-ups shouldn t be picked twice, this simple ranking doesn t work. We use linear programming. AEI (Hannover) LIGO-G GWPAW Osaka 9 / 26

10 Cas A. result (0 days coherent segment) Cas A., the youngest source: Age: 350 years Distance: 3.3 kpc Vela Jr., the closest source has uncertainty in age and distance: Age: 700 years 4300 years Distance: 0.2 kpc 0.75 kpc Cas A 0D set-up. age information involved AEI (Hannover) LIGO-G GWPAW Osaka 0 / 26

11 CasA results (four different coherent durations) Cas A age case. 5, 0, 20, 30D set-ups. 2EM budget. AEI (Hannover) LIGO-G GWPAW Osaka / 26

12 AEI (Hannover) Cas A, age case. LIGO-G Combine 5, 0, 20, 30D set-ups GWPAW Osaka 2 / 26 Cas A: Optimization over four set-ups (age case) Linear Programming applied here

13 Optimization over multiple sources & set-ups (age case) put three sources in one bank, the cells distribution AEI (Hannover) LIGO-G GWPAW Osaka 3 / 26

14 the first important thing we have learned The best set-up for coherent segment is longer than we thought. Previously, we use 5.8 days in Cas A search. Our result shows the best set-up in coherent segment duration is between 0 days to 30 days. AEI (Hannover) LIGO-G GWPAW Osaka 4 / 26

15 what we have learned: age influence Figure: R and C vary with age. Vela Jr., 20 days coherent segment. AEI (Hannover) LIGO-G GWPAW Osaka 5 / 26

16 what we have learned: Vela Jr. beats Cas A Comparison Between Vela Jr. and Cas A(age case, 0D) AEI (Hannover) LIGO-G GWPAW Osaka 6 / 26

17 Figure: S6 data (300D), 6EM budget, 5, 0, 20, 30D days coherent segment AEI (Hannover) LIGO-G GWPAW Osaka 7 / 26 what we have learned: S6 data is much worse than O C=6EM R= C=6EM R= f (Hz/s) f (Hz/s) f (Hz/s) f (Hz) C=6EM R= f (Hz) f (Hz/s) f (Hz) C=6EM R= f (Hz)

18 Figure: O data (90D), 6EM budget, 5, 0, 8, 30D days coherent segment AEI (Hannover) LIGO-G GWPAW Osaka 8 / 26 what we have learned: O data is promising C=0.7EM R= C=0.7EM R= f (Hz/s) f (Hz/s) f (Hz/s) f (Hz) C=2.6EM R= f (Hz) f (Hz/s) f (Hz) C=6EM R= f (Hz)

19 Conclusions This is an efficient and general method/system to determine the set-up, parameter space and astrophysical targets for directed searches. Thus maximize the probability constrained by computing power budget. It is flexible for prior. We can use this to investigate how does prior influence detection probability. Use to set up next directed searches. AEI (Hannover) LIGO-G GWPAW Osaka 9 / 26

20 Thank You AEI (Hannover) LIGO-G GWPAW Osaka 20 / 26

21 Astrophysical Sources Table: directed targets from LSC-CW list maintained by B. Owen SNR G name Other name Point source J Size( ) Dkpc τkyr 0 25 h age < W < C < W5C DA DA < Yougest.7 2. Cas A IC Closest Vela Jr MSH -6A MSH > < MSH <5 > RCW (27).4 AEI (Hannover) LIGO-G GWPAW Osaka 2 / 26

22 Vela Jr. result (0 days coherent segment) Vela Jr. 0D set-up. age and non age cases. AEI (Hannover) LIGO-G GWPAW Osaka 22 / 26

23 Cas A 0D set-up. age and non age cases. AEI (Hannover) LIGO-G GWPAW Osaka 23 / 26

24 Optimization over multiple sources & set-ups (non age) Closest case (top 3 plots) for Vela Jr. and farthest (bottom 3 plots) case for Vela Jr. respectively. AEI (Hannover) LIGO-G GWPAW Osaka 24 / 26

25 Optimization over multiple sources & set-ups (age case) Closest & youngest (CY) case (top 3 plots) for Vela Jr. and farthest & oldest (FO) (bottom 3 plots) case for Vela Jr. respectively. AEI (Hannover) LIGO-G GWPAW Osaka 25 / 26

26 Results Table: R result in no age information case Name Dkpc R (5D) R (0D) R (20D) R (30D) R (4 set-ups,2em) R (4 set-ups,24em) R (4 set-ups,48em) Cas A IC G Vela Jr Vela Jr Top 3 (0.2 kpc) Top 3 (0.75 kpc) Table: R result in age information case Name Dkpc τkyr R (5D) R (0D) R (20D) R (30D) R (4 set-ups,2em) R (4 set-ups,24em) R (4 set-ups,48em) Cas A G G Vela Jr Vela Jr (6.6EM) (5.EM) (8.5EM) Vela Jr (6.6EM) (5.EM) (8.5EM) Top 3 (CY) Top 3 (FO) AEI (Hannover) LIGO-G GWPAW Osaka 26 / 26