全然上手くいかん！
ゆっくり少しずつテスト。
まず、地球を、完全な円軌道で、 1AU から。Constant time-step dt = 5E-4. 100 年回してみる。
修正１回。
一応きちんとできているように見える。a と e のエラーは1E-6 - 1E-7 くらい。
dE/E = 3.3E-7 くらいで、上昇もせず落ち着いている。
修正２回。
あかん！a がずるずる上がり、１００年で 2AU まで行ってしまう。dE/E = 0.5.
全然ダメ。修正３回も４回も似た様な結果になる。
修正のかけ方が間違ってるんではないかなー。
修正１回もしかしやや怪しい。6E4年くらいからa がずるずる上がっていって、
100,000 年では1.00001 AU になる。e は 1E-7 くらいで落ち着いてるように
見える。dE/E も10^-6 くらいで落ち着いているが、8E4 年位から変な
跳ね方をし始める。
やっぱり一度コードをシンプルにして、階層かステップ等もなしにして
小久保さんのプロットを忠実に再現する方向に集中してみよう。
vendredi 30 mai 2008
Hermite Corrector II.
修正を一度だけかけると、a と e が少しずつ下がっていく。Kokubo, Yoshinaga & Makino (1998) の結果と同じ。
しかし修正を二度かけると、a も e も上がっていく。これは修正のどこかで計算ミスしている筈だ。
もう一度修正のかけ方を復習。
新しい加速度と、加速度の一次微分を使って、エルミート補完式から
a(2) と a(3) を求める。これが修正子。
これを、修正式を使って、予測子に足してやる。これで予測子 x_{c,i} と v_{c,i} が
求まる。
この予測子を使って、もう一度中心星からの加速度と一次微分を求め直す。
しかし修正を二度かけると、a も e も上がっていく。これは修正のどこかで計算ミスしている筈だ。
もう一度修正のかけ方を復習。
新しい加速度と、加速度の一次微分を使って、エルミート補完式から
a(2) と a(3) を求める。これが修正子。
これを、修正式を使って、予測子に足してやる。これで予測子 x_{c,i} と v_{c,i} が
求まる。
この予測子を使って、もう一度中心星からの加速度と一次微分を求め直す。
jeudi 29 mai 2008
Hermite Corrector
誤差が溜まっていく。何か初歩的なミスを冒している筈。
修正子は、a^(2) と a^(3) を含む。しかしこれは０にはならない。a^(2) の初めの項、aoi - a1i は０になる。しかし次の 4a(1)0 + 2a(1)1 は０にならん。という事は、修正を繰り返せば繰り返す程誤差は増えていくんじゃないの？
違う違う違う。corrector が収束していくんだ。だからどんどん足していってはいけないんだな、当然。
しかしまだ誤差が無くならない。
修正子は、a^(2) と a^(3) を含む。しかしこれは０にはならない。a^(2) の初めの項、aoi - a1i は０になる。しかし次の 4a(1)0 + 2a(1)1 は０にならん。という事は、修正を繰り返せば繰り返す程誤差は増えていくんじゃないの？
違う違う違う。corrector が収束していくんだ。だからどんどん足していってはいけないんだな、当然。
しかしまだ誤差が無くならない。
lundi 26 mai 2008
"Transiting Planets" Day 5
Conference の行われた、"The American Academy of Arts and Science" では、受賞者の感謝の手紙を飾ってあったが、その受賞者がそうそうたるメンバーだった。
Dmitri Mendeleeff
Thomas Hardy
Alfred Tennyson
Charles Darwin
Washington Irvin
Maria Mitchell
Leonhard Euler
Robert Frost
Igor Stravinsky
Albert Einstein
T.S.Eliot
Konrad Lorenz
Marian Anderson
Alexander Calder
Andrew Wyeth
Joan Miró
Jorge Luis Borges
John Cage
多くの人が手書きの手紙を寄せてあり、なかなか良い字が多かった。Thomas Jefferson なんかは acknowledge を acknolege とスペルしていたがあれは間違いだろうか。
ビッグネームが揃った割には気さくな人々が多く、興味深い交流の多い楽しい学会だった。
Dmitri Mendeleeff
Thomas Hardy
Alfred Tennyson
Charles Darwin
Washington Irvin
Maria Mitchell
Leonhard Euler
Robert Frost
Igor Stravinsky
Albert Einstein
T.S.Eliot
Konrad Lorenz
Marian Anderson
Alexander Calder
Andrew Wyeth
Joan Miró
Jorge Luis Borges
John Cage
多くの人が手書きの手紙を寄せてあり、なかなか良い字が多かった。Thomas Jefferson なんかは acknowledge を acknolege とスペルしていたがあれは間違いだろうか。
ビッグネームが揃った割には気さくな人々が多く、興味深い交流の多い楽しい学会だった。
jeudi 22 mai 2008
"Transiting Planets" Day 4
Giovanna
Little Na absorption was observed for HD209458 spectra.
Planetary albedo is < 0.25, very reflective cloud model has been ruled out.
Hubeny
There's no fundamental difference between the structures of a planet and a brown dwarf (?).
The TLUSTY code -- applicable to 50~100 K to 10,000 K. Cloud formation (Cooper et al. 2002) is included.
There are five classes of giant plaents (Sudarsky et al. 2003)
Knutson
HD209458b.....temperature inversion observed (also XO-1 b, TrES-2 b)
HD189733b......NO temperature inversion observed
TrES-4 receives high incident flux (Teq = 1,760K), and temperature inversion was also observed.
Miller-Ricci
Do super Earths retain atmospheric hydrogen?
There's temperature inversion in the Earth's stratosphere due to ozone.
GJ 581 c
5.02 Mearth, 13-day orbit, e=0.16, Teq = 370K, R = 1.6Rearth.
Due to a simple thermal-escape argument, atmospheric H should be retained due to the large surface gravity.
Scale-height model (observable from transit depth)
Absorption is deeper by 20% for H-rich planetary atmosphere than H-poor. ~20 hr / 6 transits JWST observations are needed for 100ppm detection.
Ian
Dynamics & Radiation in planetary atmosphere
Full Navier-Stokes Equation (3D), involving continuity equation, 3D momentum and thermal energy
Flux-limited model. The code is accurate in both optically thin and thick regimes.
Freedman opacity is adopted. Velocity structure would be quite different if another opacity is used (e.g., if, lower interstellar opacity is used, coriolis wind will be stronger).
Does it explain the observed temperature inversion of HD209438-b-like planets? There expected to be in fact second temperature inversion closer to the planetary surface.
Temperature inversion, and large day side/night side temperature difference may be predicted from opacity (IR / optical) and pL / pM.
Little Na absorption was observed for HD209458 spectra.
Planetary albedo is < 0.25, very reflective cloud model has been ruled out.
Hubeny
There's no fundamental difference between the structures of a planet and a brown dwarf (?).
The TLUSTY code -- applicable to 50~100 K to 10,000 K. Cloud formation (Cooper et al. 2002) is included.
There are five classes of giant plaents (Sudarsky et al. 2003)
Knutson
HD209458b.....temperature inversion observed (also XO-1 b, TrES-2 b)
HD189733b......NO temperature inversion observed
TrES-4 receives high incident flux (Teq = 1,760K), and temperature inversion was also observed.
Miller-Ricci
Do super Earths retain atmospheric hydrogen?
There's temperature inversion in the Earth's stratosphere due to ozone.
GJ 581 c
5.02 Mearth, 13-day orbit, e=0.16, Teq = 370K, R = 1.6Rearth.
Due to a simple thermal-escape argument, atmospheric H should be retained due to the large surface gravity.
Scale-height model (observable from transit depth)
Absorption is deeper by 20% for H-rich planetary atmosphere than H-poor. ~20 hr / 6 transits JWST observations are needed for 100ppm detection.
Ian
Dynamics & Radiation in planetary atmosphere
Full Navier-Stokes Equation (3D), involving continuity equation, 3D momentum and thermal energy
Flux-limited model. The code is accurate in both optically thin and thick regimes.
Freedman opacity is adopted. Velocity structure would be quite different if another opacity is used (e.g., if, lower interstellar opacity is used, coriolis wind will be stronger).
Does it explain the observed temperature inversion of HD209438-b-like planets? There expected to be in fact second temperature inversion closer to the planetary surface.
Temperature inversion, and large day side/night side temperature difference may be predicted from opacity (IR / optical) and pL / pM.
"Transiting Planets" Day 3
Tristan
M-R relations from Zapolsky & Salpeter 1969
Showed the figure of Bouchy, Monte-Carlo-simulated M-R relation sample.
Anomalously large planets:
TrES-4 b.............not too bloated. A reasonable model can be creatd.
CoRoT-2 b..........The star is variable. Planetary radius may be overestimated?
Massive Planet:
HAT-P-2 b........ 600 Mearth ice core at the center? (Baraffe)
Large solid mass:
HD149026, XO-2, OGLE-TR-56, HAT-P-2, etc.
Giant impacts and core merger can be a possible explanation for massive cores.
Alternatively, evaporation of close-in planets, perhaps incorporating tidal effects,
is also possible.
Sara Seager
Mercury's core is 60% of the mass.
Two competing theories for Fe:
Fe is expected to sink toward the core.
At the same time, it can oxidize and get incorporated to the mantle. For this scenario, water content in the mantle is key to the Fe oxidization, and the amount of water depends on the radial mixing in the protoplanetary disk.
So, in the core, there should be a simple inverse relation for Fe and H2O. A coreless Earth should have Fe-rich mantle.
Willie Benz
Monte Carlo simulation of planet formation and migration (Pollack 1996)
Yanqin
The 3-day pile up in the orbital period histogram should be a natural outcome of
Kozai migration.
Deming
Spectroscopic observations:
HD209458.............Grillmair 2007, Richardson 2007, Swain 2008
IRAC broad-band spectrum requires temperature inversion in the atmosphere.
(and flatness of the water absorption)
GJ 436 b...................secondary eclipse observation
Teq = 640K Tobs = 712K
Spitzer G05, multiple-eclipse, around-the-orbit observations
EPOXI is currently observing multiple transits from space.
Eric Agol
Precise transit-timing and transit depth variations. For the TTV due to a non-resonant, eccentric perturber, dt = P1 e2 m2/m0 P1 / P2. It is 33 sec for WASP-9, and 0.3 sec for CoRoT-Exo-1.
Jackson
Tidal circularization timescale has been historically underestimated.
Tidal heating rate is not constant during migration (isn't that obvious?)
So, external perturber may not be necessary to explain eccentric close-in planets (e.g., GJ 436 b).
Also, past tidal heating bloats up planets because tidal heating takes ~Gyr to get out (!! reasoning unclear).
Laughlin
HD80606 transit campain (pericenter distance is 6.5 Rstar). Pseudo-spin-orbit synchronization is expected.
M-R relations from Zapolsky & Salpeter 1969
Showed the figure of Bouchy, Monte-Carlo-simulated M-R relation sample.
Anomalously large planets:
TrES-4 b.............not too bloated. A reasonable model can be creatd.
CoRoT-2 b..........The star is variable. Planetary radius may be overestimated?
Massive Planet:
HAT-P-2 b........ 600 Mearth ice core at the center? (Baraffe)
Large solid mass:
HD149026, XO-2, OGLE-TR-56, HAT-P-2, etc.
Giant impacts and core merger can be a possible explanation for massive cores.
Alternatively, evaporation of close-in planets, perhaps incorporating tidal effects,
is also possible.
Sara Seager
Mercury's core is 60% of the mass.
Two competing theories for Fe:
Fe is expected to sink toward the core.
At the same time, it can oxidize and get incorporated to the mantle. For this scenario, water content in the mantle is key to the Fe oxidization, and the amount of water depends on the radial mixing in the protoplanetary disk.
So, in the core, there should be a simple inverse relation for Fe and H2O. A coreless Earth should have Fe-rich mantle.
Willie Benz
Monte Carlo simulation of planet formation and migration (Pollack 1996)
Yanqin
The 3-day pile up in the orbital period histogram should be a natural outcome of
Kozai migration.
Deming
Spectroscopic observations:
HD209458.............Grillmair 2007, Richardson 2007, Swain 2008
IRAC broad-band spectrum requires temperature inversion in the atmosphere.
(and flatness of the water absorption)
GJ 436 b...................secondary eclipse observation
Teq = 640K Tobs = 712K
Spitzer G05, multiple-eclipse, around-the-orbit observations
EPOXI is currently observing multiple transits from space.
Eric Agol
Precise transit-timing and transit depth variations. For the TTV due to a non-resonant, eccentric perturber, dt = P1 e2 m2/m0 P1 / P2. It is 33 sec for WASP-9, and 0.3 sec for CoRoT-Exo-1.
Jackson
Tidal circularization timescale has been historically underestimated.
Tidal heating rate is not constant during migration (isn't that obvious?)
So, external perturber may not be necessary to explain eccentric close-in planets (e.g., GJ 436 b).
Also, past tidal heating bloats up planets because tidal heating takes ~Gyr to get out (!! reasoning unclear).
Laughlin
HD80606 transit campain (pericenter distance is 6.5 Rstar). Pseudo-spin-orbit synchronization is expected.
mardi 20 mai 2008
"Transiting Planets" Day 2
Queloz
Euler Swiss Telescope (Transit follow-up)
One system with a transiting planet with a binary companion at 2.6 AU
with 0.25 Msun?
Konacki
Circumbinary planet? (not yet confirmed)
A. Howard
Keck eta-Earth Project Surveying 1,330 F-M stars
GJ 317, 581, 876, 674, 849, 436, 176
GJ 176 (2008)
10-day, 28Mearth (Endl, HET)
NOTHING seen at 10-day orbit from Keck
GJ 436 b
Linear residual trend is going away? (Not seen in the latest Keck data)
Residuals in the periodogram indicates presence of 3-20 Mearth planet
GJ 317 b (JohnJohn)
1.2 Mj, ~2-yr orbit
Residual 12.6 m/s --- planet c at P > 7-yr?
Lovis
Hot Neptune and super Earth
HARPS rad-vel searches: ~400 non-active, slowly-rotating FGK dwarfs (since 2004)
Focus on smaller sample of stars, but with high-cadence observations
Mu Aracni: 9.6-day hot Neptune
HD69830: With the latest data, orbital parameters remained unchanged
45 candidates with < 30 Mearth, < 50-day
- 4-day e=0 22.8 Mearth
- 2.34-day, e= 0-0.2, 5.8 Mearth
- 3.8-day, 4 Mearth
- 25.6-day, 30 Mearth
- 7.44-day, e=0.65, 10 Mearth
- 46-day, e=0.23, 20 Mearth
- 40-day, e=0.5, 10 Mearth
- triple-super-Earth system
80% of the candidates seem to be members of multiple planets
Hot Neptune / Super Earth
- 10-day peak---is the orbital migration for smaller planets different?
The peak for hot Jupiters is 3 days.
- Large orbital eccentricity seems common.
- Planet occurrence is high --- ~ 30%
- They already made it to the top-priority space-based transit target list
Dimitar
HARPS-N Synergy w/ Kepler
10 cm/s precision
Calibration is improved compared to HARPS (~1/2 of the HARPS uncertainty was attributed to the reference)
Euler Swiss Telescope (Transit follow-up)
One system with a transiting planet with a binary companion at 2.6 AU
with 0.25 Msun?
Konacki
Circumbinary planet? (not yet confirmed)
A. Howard
Keck eta-Earth Project Surveying 1,330 F-M stars
GJ 317, 581, 876, 674, 849, 436, 176
GJ 176 (2008)
10-day, 28Mearth (Endl, HET)
NOTHING seen at 10-day orbit from Keck
GJ 436 b
Linear residual trend is going away? (Not seen in the latest Keck data)
Residuals in the periodogram indicates presence of 3-20 Mearth planet
GJ 317 b (JohnJohn)
1.2 Mj, ~2-yr orbit
Residual 12.6 m/s --- planet c at P > 7-yr?
Lovis
Hot Neptune and super Earth
HARPS rad-vel searches: ~400 non-active, slowly-rotating FGK dwarfs (since 2004)
Focus on smaller sample of stars, but with high-cadence observations
Mu Aracni: 9.6-day hot Neptune
HD69830: With the latest data, orbital parameters remained unchanged
45 candidates with < 30 Mearth, < 50-day
- 4-day e=0 22.8 Mearth
- 2.34-day, e= 0-0.2, 5.8 Mearth
- 3.8-day, 4 Mearth
- 25.6-day, 30 Mearth
- 7.44-day, e=0.65, 10 Mearth
- 46-day, e=0.23, 20 Mearth
- 40-day, e=0.5, 10 Mearth
- triple-super-Earth system
80% of the candidates seem to be members of multiple planets
Hot Neptune / Super Earth
- 10-day peak---is the orbital migration for smaller planets different?
The peak for hot Jupiters is 3 days.
- Large orbital eccentricity seems common.
- Planet occurrence is high --- ~ 30%
- They already made it to the top-priority space-based transit target list
Dimitar
HARPS-N Synergy w/ Kepler
10 cm/s precision
Calibration is improved compared to HARPS (~1/2 of the HARPS uncertainty was attributed to the reference)
"Transiting Planets" Day 1
Hébrard (Poster)
XO-3 spin-orbit misalignment 90 deg (70 +/- 10?)
Large air-mass (20 deg from the horizon) could have affected the observation
Many posters on transit timing variation.
XO-3 spin-orbit misalignment 90 deg (70 +/- 10?)
Large air-mass (20 deg from the horizon) could have affected the observation
Many posters on transit timing variation.
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