Transformations of galaxies. III. Supplemental figures Joshua E. Barnes ∗, † October 9, 2015 Abstract These figures supplement the MS “Transformations of galaxies. III. Encounter dynamics and tidal response as functions of galaxy structure”. Parameter Codes In some of the following plots, individual simulations are identified by four-digit code numbers, where each hexadecimal digit corresponds to a different parameter. The format of this code is FCDP , where (F, C, D, P ) are single digits specifying values of (f L ,c h , α d a h ,r p /a h ), respectively. The mapping from digits to parameter values is: digit f L c h α d a h r p /a h 1 0.2 6.0 2 4.8 3 3.75 4 0.1 16.0 3.0 0.5 5 2.4 0.625 6 1.875 0.8 7 0.05 8.0 1.5 1.0 8 1.2 1.25 9 1.6 A 4.0 2.0 For example, code 7736 implies parameters (f L ,c h , α d a h ,r p /a h ) = (0.05, 8.0, 3.75, 0.8). Likewise, pa- rameters (f L ,c h , α d a h ,r p /a h ) = (0.2, 4.0, 3.0, 2.0) imply code 1A4A. Note that successive parameter values are spaced by factors very close to 3 √ 2, and that room is available for future expansion. Ital- icized parameter values for α d a h were included in stability tests but were not actually used in the experiments. ∗ Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA † Yukawa Institute for Theoretical Physics, Kyoto University, Sakyo-ku, Kyoto 606-8502 Japan 1
Transcript
Transformations of galaxies. III. Supplemental figures
Joshua E. Barnes∗,†
October 9, 2015
Abstract
These figures supplement the MS “Transformations of galaxies. III. Encounter dynamicsand tidal response as functions of galaxy structure”.
Parameter Codes
In some of the following plots, individual simulations are identified by four-digit code numbers, whereeach hexadecimal digit corresponds to a different parameter. The format of this code is FCDP , where(F,C,D, P ) are single digits specifying values of (fL, ch,αdah, rp/ah), respectively. The mapping fromdigits to parameter values is:
For example, code 7736 implies parameters (fL, ch,αdah, rp/ah) = (0.05, 8.0, 3.75, 0.8). Likewise, pa-rameters (fL, ch,αdah, rp/ah) = (0.2, 4.0, 3.0, 2.0) imply code 1A4A. Note that successive parametervalues are spaced by factors very close to 3
√2, and that room is available for future expansion. Ital-
icized parameter values for αdah were included in stability tests but were not actually used in theexperiments.
∗Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA†Yukawa Institute for Theoretical Physics, Kyoto University, Sakyo-ku, Kyoto 606-8502 Japan
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Figure 1: Scatter plot showing relationship between interpenetration and effective argument of pe-riapse for the inclined disc, ωeff
2 (in degrees). Symbol type indicates ch, while color indicates rp/ah;see MS Figs. 3 and 6. The effective argument has a roughly linear relationship with the log of theinterpenetration factor: ωeff
2 ≃ +16.3◦ − 31.2◦ log10(R1/2/rp).
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Figure 2: Expanded version of MS Fig. 5, showing relationships between interpenetration and orbitdecay. Here R1/4, R1/2, and R3/4 are the radii containing 25, 50, and 75 percent, respectively, of thetotal mass. Likewise, t1/4, t1/2, and t3/4 are circular orbital periods at these radii. The middle panel,which reproduces MS Fig. 5, shows the least scatter.
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Figure 3: Response of i = 0◦ (top) and i = 71◦ (bottom) discs in rp/ah = 0.5 encounters, shown onerotation period after first passage.
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Figure 4: Response of i = 0◦ (top) and i = 71◦ (bottom) discs in rp/ah = 2 encounters, shown onerotation period after first passage.
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Figure 5: Scatter plot of total tidal fraction (fbridge + ftail) plotted against SW’s escape parameterE . Separate results are shown for the i = 0◦ (left) and i = 71◦ (right) discs. Symbol type and colorsmatch MS Fig. 12. This figure may be compared to SW’s fig. 10; the dashed lines represent theirestimated upper limit on the tidal response. The present study adopts a more liberal definition oftidal material and therefore obtains larger tidal fractions, but the trends seen here are consistentwith those found by SW.
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Figure
6:Tailevolution
diagn
ostics
fori=
0◦discs
inr p/a
h=
1encounters.
Eachpan
elislabeled
withasimulation
code.
Black
curve:
survivingtailfraction
,log 1
0(f
tail)+3(see
Fig.14).
Bluepoints:
tailreaccretionrate,log 1
0(−
dftail/d
t).Green
points:
averageap
ocentric
radiusof
bod
iescurrentlyundergoingtail-loo
ptran
sition
.Red
points:
averagepericentric
radiusof
bod
iescurrentlyundergoingtail-loo
ptran
sition
.Allof
thesevalues
fallin
therange
[0,3]an
dareplotted
onacommon
scale.
7
Figure
7:Tailevolution
diagn
ostics
fori=
71◦discs
inr p/a
h=
1encounters.
Eachpan
elislabeled
withasimulation
code.
Black
curve:
survivingtailfraction
,log 1
0(f
tail)+3(see
Fig.14).
Bluepoints:
tailreaccretionrate,log 1
0(−
dftail/d
t).Green
points:
averageap
ocentric
radiusof
bod
iescurrentlyundergoingtail-loo
ptran
sition
.Red
points:
averagepericentric
radiusof
bod
iescurrentlyundergoingtail-loo
ptran
sition
.Allof
thesevalues
fallin
therange
[0,3]an
dareplotted
onacommon
scale.
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Figure 8: Scatter plots showing relationship between fractions of tail material not yet reaccreted andηesc. As in MS Fig. 3, symbol type indicates ch, while color indicates rp/ah; solid lines show least-square fits to points of corresponding color. Left-hand and right-hand panels show results for tailsfrom i = 0◦ and i = 71◦ discs, respectively. Top row: tail fractions remaining at second pericenter.The slope of the linear fit depends systematically on rp/ah, being steepest for rp/ah = 0.5 (red) andshallowest for rp/ah = 2.0 (blue). Bottom row: tail fractions remaining after t1/4, the time requiredfor a circular orbit at the radius containing 25 percent of each galaxy model’s mass. The dependenceon rp/ah is largely eliminated; tail fallback occurs on a local dynamical timescale. Note that allpanels show a systematic trend with ch; reaccretion is faster in high-concentration halos (triangles;ch = 16) than in low-concentration halos (stars; ch = 4).
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Figure 9: Unlabeled variants of MS Fig. 18, comparing tidal configurations. Left: comparisonmade before first apocentre (tref = (tp1 + ta1)/2). Right: comparison made after first apocentre(tref = (ta1+ tp2)/2). Both versions display the same overall pattern, but the discrimination betweendifferent encounters improves at later times.
Figure 10: Unlabeled variants of MS Fig. 18, comparing tidal configurations. Left: comparisonmade using images showing only bodies from the i = 0◦ disc. Right: comparison made using imagesshowing only bodies from the i = 71◦ disc. Both discs yield similar patterns of degeneracy.
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Figure 11: Three pairs of encounters undergoing violent orbit decay. The top pair are the mostsimilar; both δfIJ
tail and DIJmin increase moving down the page. Bottom plot shows upper-right panel
of MS Fig. 21, with these three pairs marked.
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Figure 12: Three pairs of encounters undergoing gentle orbit decay. The top pair are the mostsimilar; both δfIJ
tail and DIJmin increase moving down the page. Bottom plot shows lower-left panel of
