PULSAR FORMATION RATES HOW HOW ? ? - PDF document

✟ ★ ✧ ★ ✬ ★ ✰ ✩ ✲ ✩ ✫ ★ ✬ ✳ ✮ ✴ ✱ ✫ ✰ ✧ ✥ ☎ ✆ ✞ ✟ ✟ ✞ ✄ ✑ ✁ ✣ ✄ ✜ ✆ ✟ ✟ ✆ ✟ ✰ ✵ ✝ ✆ ✷ ✞ ✠ ✆ ✝ ✞ ✍ ✆ ✰ ✟ ✝ ✞ ✍ ✌ ✝ ✆ ✵ ★ ✶ ✧ ✰ ✮ ✩ ✫ ★ ✬ ✰ ★ ✬ ✤ ✱ ✬ ★ ✰ ✩ ✲ ✥ ✄ ✍ ✆ ✓ ✍ ☎ ✄ ☞ ✆ ✎ ✄ ✟ ✠ ✟ ✚ ✁ ☛ ✚ ✛ ✌ ☞ ✆ ✟ ✄ ☎ ✆ ✁ ✝ ✞ ✆ ✄ ✆ ✠ ✄ ✡ ✟ ✆ ✁ ☛ ✟ ✆ ✎ ✝ ✝ ✜ ✆ ✁ ✁ ✄ ✆ ✢ ✑ ✟ ✠ ✌ ✜ ✜ ✄ ✝ ✄ ✆ ✁ ✠ ✟ ☞ ✠ ✆ ✑ ✄ ✞ ✝ ✜ ✞ PULSAR FORMATION RATES HOW HOW ✎✏✆ ? ? ✗✙✘ ✤✯✱ ✔✖✕ ✤✯✮ ✤✯✮ ★✭✬ ✞✒✑ ★✪✩ ✤✦✥ �✂✁

❑ ❖ ❑ ▲ ❱ ▲ ◗ ❍ ❑ ❨ ❄ ❆ ❉ ❇ ❩ ❙ ❳ ❳ ▲ ❆ ❄ ◗ ❲ ❄ ❏ ▼ ❄ ❆ P ▲ ❇ ❄ ❏ ▼ ❬ ❯ P ❇ ❭ ❈ ❆ ❲ ❄ ◗ ❄ ▼ ❪ ◗ ▼ P ❯ ❄ ❆ ❈ ❄ ❩ ◆ ▲ ❬ ❉ ▼ ◗ ❬ ❉ ▲ ❯ ❬ ❖ ❯ ▲ ❇ ▼ ✽ ❄ ❄ ❉ ▲ ❊ ❉ ❇ ❄ ❏ ❄ ❉ ■ ✻ ● ◆ ❋ ✾ ❈ ❇ ❆ ✿ ❂ ✿ ✾ ❀ ✹ ❁ ▼ ❉ ❀ ✻ ◗ ❄ ❲ ❄ ◗ ▼ ◆ ❊ ❱ ▲ ❯ ▲ ❉ ■ ❆ ❈ ❇ ❚ ✼ ◆ ▼ ❄◗ P ❑ ❖ ❆ ❄ PULSAR FORMATION RATES HOW HOW ? ? ❈✒❑ ■❅❄ ❈✒❍ ✽✦✾ ❉✦❊ ❘✖❙ ✸✺✹ ❃❅❄

❦ ❝ ❢ ❜ ❛ ❡ ❢ ❧ ✐ ♥ ❧ ❧ ❥ ❢ ❡ ❜ ❢ ❜ ❣ ♠ ❣ ❡ ❧ ❜ ♠ ❜ ❢ ❛ ❝ ❝ ❴ ❧ ❴ ✐ ❥ ❦ ❧ ❣ ❧ Radio Pulsars NS-NS in Merger NS-NS binaries Rate Estimates Narayan et al. '91; Phinney '91; Scale-factor calculations: Curran & Lorimer '95; Arzoumanian et al. '99; VK et al. '01 ❫❵❴ ❜❞❝ ❢❤❣ ❜❞❝ ♥♣♦ small - number observed sample (2 NS -NS in Galactic field) PSR population dominated by faint objects Robust lower limit for the MW: 1 per Myr Upward correction factor for faint PSRs: ~ 1-500

➄ ➄ ❸ q ⑤ ⑧ ⑥ ⑨ ⑧ ⑤ ❺ ✈ ✇ ➜ s ➅ ✉ ➇ ➅ ➟ ➣ s ❾ ➀ ✈ ✉ ❺ ➐ ➣ ❷ ❺ s ✉ ❷ ➊ ✉ ➌ ❷ ➀ ⑨ ❺ ❷ s ❸ s ➣ ➥ ➇ ➣ ❷ s ❾ ⑤ ➙ ❷ ➔ ✈ ❸ ❾ ➇ ➅ ➛ ✇ s ❺ ❸ → ❷ ⑤ ❻ ✈ ✉ ❷ ⑤ ❸ ⑤ ❸ ⑤ ⑧ ❻ ✉ ✉ ➜ ➟ ⑤ ❸ ❽ ✇ ➜ ❺ ➢ ➡ ➤ ➟ ③ ✈ ④ ➠ ➟ ➙ ➀ ✇ s ❷ ✉ ✉ s ❸ ❽ ❷ ✉ ❺ ❾ ❷ ⑨ ➅ ❺ ❷ s ❸ → ✈ ❾ ❷ ➔ ✈ ✇ ➜ ➄ ➣ ❷ ✉ ⑤ ➁ ⑨ ❺ ❷ s ❸ ✇ s ④ ⑨ ⑧ ⑤ ❺ ✈ ⑤ ❷ ⑧ ⑤ ➂ ❻ ➃ ❷ ❺ r ➊ ➅ ➉ ➉ ➊ ➋ ➀ ➧ ➍ ❽ ➟ ➨ ➜ ✇ ✈ ➔ ❷ ❾ q ✈ s ✉ ✈ ③ ✉ ✉ ④⑤ ⑥ ✈ ⑦ ❽ ❶ ❸ s ✉ ❷ ⑤ ❽ ❷ ➊ ➊ ✈ ⑨ ✈ ⑥ ❺ ❷ s ❸ ⑤ ❸ ❽ ④ ❾ s ❽ ⑥ ✈ ✈ s ➀ ✉ ✈ ❾ ➔ ✈ ❽ ✉ ⑤ ❶ ④ ⑧ ❺ ❽ ➦ ① ⑧ ❷ ➒ ✈ ➓ ➓ ④ ⑨ ⑧ ✉ ⑤ ❾ ✉ ❷ ❻ ❶ ⑨ ⑧ ⑤ ❺ ✈ ✇ ① ③ ✉ ⑨ ❾ ➔ ✈ ✈ Kim, VK, Lorimer '03 Probability Calculation Distribution of Rate NS-NS rate es timates with Monte Carlo s imulations It is pos s ible to as s ign s tatis tical s ignificance to ③➑➡ ❺❿❾ ③➩➨➭➫ ➏➑➐ ➄➆➅ ❺❼❻ ➌➎➍ ❷❹❸ ➄➆➅➈➇ ⑧⑩⑨ "Forward" Statistical Approach ↔❹↕ ➊➞➝ ➅➈➇ ✇②① ❺❿❾ rts

➼ ➼ ❮ ➴ ➘ ➶ ❒ ❐ ➼ ➼ ➮ ➬ ➷ ➼ ➾ ➼ ➻ ➯ ➯ ➲ ➵ ➺ ➸ ➲ ➳ PSR B1913+16 Distribution of number of objects in ➳❤➵ observed samples: Poisson ➽➚➾ ➘t➴ ➪➹➶ ➱✙✃ Likelihood of current sample: P(1 ; ) = exp(- )

Ý Ý × â Ý à á × ß í ß Ý ã Ü × × Ü Ý Ü ê Ô ❰ Ï Ð Ó Ü ð ï Ô Õ Ö × Ø î Û ë PSR B1913+16 The mean of the Poisson distribution ÑtÒ is linearly proportional to the total number of PSRs in the Galaxy: ×ÞÝ❿ß Ù✖Ú Using Bayes' theorem we calculate the probability distribution: âäã 2 á✙ì åçæ åéè and the most likely value is: = 1/

✢ ✖ ñ ✟ ✁ ✣ ó ✍ ☛ ☞ ✒ ✗ ✜ ✔ ✘ ✗ ✔ ✙ ✒ ✚ ✔ ✛ ó ✆ ✁ ñ þ ÿ ✁ ✥ ✆ ó ✤ ÷ õ õ ÷ õ ✁ ò ò ✆ ó ý ☛✌☞ ✓✕✔ ✎✑✏ ôöõ øúùüû ñ➑ò ✂☎✄ ø ✡✠ ñ ✞✝ Using the probability distribution we can calculate the most likely rate as well as the ranges of rates at various confidence levels

✴ ✭ ✮ ✪ ✲ ✲ ✩ ✾ ✯✱✰ ✪✬✫ ✦★✧ ✩✳✲ Dependence of most likely coalescence rate on the PSR LF parameters: ✴✶✵ ✴✸✷ ✹✻✺ ✴✽✼ ✿❁❀ R peak is mostly insensitive to the spatial distribution parameters

◗ ❭ ◆ ▲ ❘ ❙❚ ❙ ❲ ❳ ❯ ❙ ◗ ❘ ❪ ❪ ❘ ▲ ▼ ◆ P ◆ ◗ ❭ ❘ P ▲ ❪ ❂ ◗ ❂ ❃ ◆ ❃ ❄ ❇ ❅ ❃ ❈ ❇ ❉ ❊ ❃ ❊ ❋ ● ❋ P ◆ ▼ Typical uncertainties: ❏✡❑ ❯❆❱ ❨❬❩ ▼❖◆ ❏❴❫ Current expectations for most likely advanced (initial) LIGO detection rates of NS-NS inspiral events ❄❆❅ ❄■❍ R det 4-100 (1/yr) (1-25) x 10 -3

② ⑦ ⑨ ⑨ ⑧ ⑦ ⑥ ③ ❷ ❼ ❺ ⑦ ④ ❺ ❻ ➇ ❶ ➋ ➌ ⑧ ❣ ① ❡ ❥ ❡ ✇ q ♦ ♥ ❝ ❜ ⑩ ❷❸ ♠ ⑦ ③ ➅ ⑧ ⑨ ➄ ➃ ➂ ➁ ⑨ ❾ ❷ ⑩ ❿ ⑩ ⑩ ❹ ❺ ⑦ ❿ ③ ❾ ⑧ ❼ ④ ❾ ❶ ❽ ➀ ❺ ③ ❝ t ➆ ❦ r t s ❦ q ❺ ♥ ⑦ ❜ ❥ ♦ ♥ ❜ ♠ ❢ ❡ ❡ ➍ ✐ ❤ ❣ ❢ ❡ ⑨ ❛ ❵ ❿ ❼ ⑧ ➎ ❤ ❢ ❝ ❝ ✈ q ❢ ❡ q ❼ ♥ q ❥ ❛ ❛ ✐ ✉ ❡ ❡ ❡ ♦ ♥ ❢ q ♥ ❢ t ♦ ❦ ❢ t q ❥ ❛ ❺ Radio Pulsars NS-WD in Merger NS-WD binaries Rate Estimates ❜❞❝ ❥❧❦ ❜❞r ❜❞r ♣❁q PSR J0751+1807 (Lundgren et al. '95) PSR J1757- 5322 PSR J1141- 6545 (Edwards & Bailes '01) (Kaspi et al. '00) ③⑤④ ❻★❼ ③❞➀ PSR J1141- 6545 ➈➊➉

➐ ➢ ➛ ➛ ➐ ➫ ➔ ➠ ➢ ➦ ➳ ➵ ➸ ➑ ➫ ➺ ➐ ➻ ➫ ➐ ➦ ➫ ➐ ➓ ➑ ➔ ➢ ➦➩ ➑ ➠ ➒ ➓ ➑ → ➣ ↔ ➐ ➛ ➛ ➟ ➠ ➔ ➥ ➔ ➑ ➦ ➝ ➧ ➐ ➑ ➨ ➜➞➝ ➔✬➐ ➡➤➢ ↕✸➙ ➏■➐ ➭✌➯■➲

Õ Ò Õ Ý ✃ Ö Þ Ð Õ Ó Ó Ï Ð ❮ Õ à Ù Ö Ü ✃ Ô ✃ Ö ✃ Õ Ö × Ü Ô ✃ Õ Ö Ó ✃ Û Ó Û ❰ ❮ Ü Ô ✃ ➚ Ù × Õ Ô ✃ á ❮ Ó ❰ Õ ❮ Ü × ❒ Õ Ö Ð × Ü ❮ ❰ Ô Ò Ù Ð × Ð Õ Ö Ò ❰ Ü Ö Ð Õ Ú Ó × Û Ó ❒ Ð ❮ Õ Ú Ó × Û ❰ Õ Ó Ð Û × Ó Ú Ö ❮ ✃ Ô Õ ➮ ➪ ➪ ➷ ➚ ➹ ➮ ➮ Ö ❒ ÒÓ ❮ Ï Ô Ù ❰ Ð Ô Ü ❒ Ð ✃ Ô Õ Ö Ô Õ ❒ ß Û Û ❮ Ý × Ü Ö × Ü × Ï Ù Ô ✃ Ü × Ý × Ó ❒ Ü Ù Ô Þ Ö ➴➬➷ ÖØ× Ô✽Õ ➶➘➹ ÏÑÐ ❮✬❰ ➼➾➽ Ô✽Õ ÏÑÐ ❮✬❰ ➱❐✃