31_7_15_reu_presentation_delavega.pdf
TRANSCRIPT
Phase Wrapping of Epicyclic Perturba6ons in the Wobbly Galaxy
31 July 2015 Advisor: Alice Quillen
Alexander de la Vega, Johns Hopkins University
Introduc6on -‐ I • Recent surveys in solar neighbourhood show mean velocity gradients • Typically <Vi> ≈ ± 5 – 15 km s-‐1 • Show wavelike paUerns of compression and rarefac6on • Vary with height away from Galac6c mid-‐plane
Williams et al. (2013) Carlin et al. (2013)
Introduc6on -‐ II • Gradients thought to arise from self-‐gravita6ng oscilla6ons in the disc • Known as ‘bending’ (L) and ‘breathing’ (R) modes
• Widrow et al. (2014) apply the following linear fit for ver6cal veloci6es:
AZ = breathing, BZ = bending
• Sun et al. (2015) ‘confirm’ breathing and bending modes near Sun • -‐15 < AZ < 2 km s-‐1 kpc-‐1, -‐5 < BZ < 15 km s-‐1
Weinberg (2001)
A slight problem…
• Breathing and bending mode theory has only been worked out in 1D (Z) • Theory is a liUle complicated – read Weinberg (1991) if you dare • Bending modes predict distance between <Z> maxima ≈ 10 kpc at R¤
• N-‐body simula6ons show much smaller distance • Is there another, perhaps simpler, explana6on? • Epicyclic Phase Wrapping, perhaps?
Theory -‐ Epicycles • Originally developed by Apollonius and Hipparchus c. 200 B.C.E. • Most galaxies look like discs, so we use an axisymmetric galac6c poten6al • Implies that the Lagrangian has cylindrical coordinates (R, θ, Z) • Most stars on nearly circular orbits – 1st order approx. is to use epicycles:
Rg = guiding radius, ar, az = amplitudes, κ = epicyclic (or radial) freq., ν = ver6cal freq., φr, φz = phases
In X, Y
In R, Z
Theory – Epicyclic Phase Wrapping (EPW)
• Perturbing a region of stars could cause them to all have same epicyclic phase
• Over 6me the same region would see a large spread in phase angles • Due to κ and ν dependence on R, Lz, eccentricity & inclina6on • Quillen et al. (2009) find this also leads to spirals and warps in the disc • Could EPW also cause velocity gradients? • If so, how do we perturb the disc?
hUp://astro.pas.rochester.edu/~aquillen/mytalks/yale.pptx Quillen et al. (2009)
SagiUarius Dwarf Galaxy (SagD)
• Discovered by Ibata et al. (1994) • Currently 28 kpc from Sun • Purcell et al. (2011) claim encounter with SagD led to spiral arms
o Used masses 1010.5, 1011 M¤ in N-‐body simula6ons o Last pericentre 0.8 Gyr ago, at distance of 15 kpc
• Widrow et al. (2014) – N-‐body with 6 × 109 M¤ satellite passing through disc o Supposedly excites ‘bending’ and ‘breathing’ modes o Find velocity gradients
Methods • Populate disc with 107 stars:
o Uniformly distributed radii, azimuths and epicyclic phases and amplitudes o Ini6al radial and ver6cal dispersion from Nordström et al. (2004)
• We consider two encounters with SagD: o E2: 2.2 Gyr ago, through the disc, with Md = 5 × 1010 M¤ o E1: 1.1 Gyr ago, above the disc, with Md = 2.5 × 1010 M¤
• Instantaneously perturb stars with hyperbolic orbit approx.: o Done separately for each encounter o Prop. to SagD mass, inversely prop. to SagD velocity
• Integrate to present day in fixed poten6al o Used python test-‐par6cle suite galpy (Bovy 2015) o Test-‐par6cles are MASSLESS (ergo no self-‐gravity) o Study effects from EPW in isola6on
Ini6al Condi6ons at 6me of Encounter • For the E2 encounter:
o Epicyclic phases off by π for <VR> and <VZ>
• For the E1 encounter: o Nearly homogeneous <VZ>, some phase disparity by π for <VR>
A{er Integra6on – E2
• Resul6ng structure is smeared due to phase wrapping over 2.2 Gyr • A lot of mixing as ini6al veloci6es out of phase with each other by π • Magnitude of gradients reduced
A{er Integra6on – E1
• Structure very similar to Gómez et al. (2013) – N-‐body with SagD passage • Gradients of similar magnitude to observed values! • More wrapped in <VR> due to ini6al phase discrepancies • Seems to excite ‘bending’ and ‘breathing’ modes – but there’s no self-‐gravity!
Gradients – E1
• Observed (L) and E1 (R) gradients • Couldn’t find region that exactly matched all observed gradients near Sun • Rota6on period at R¤ is 0.2 Gyr; off by 0.1 Gyr with SagD, off by π in azimuth
Williams et al. (2013)
Dynamical Interpreta6on
• Perturbed stars shear azimuthally and radially • For E1, nearly all perturbed stars have same φZ, so they shear ver6cally • Unperturbed stars shear azimuthally at same rate; remain outside of
perturbed region • When perturbed stars mix with unperturbed stars, we get gradients! • Difference in ini6al <VR>, <Vθ> produces two popula6ons of perturbed stars • Can mix with each other and with unperturbed stars; 2x oscilla6ons
Caveats
• Now that we’ve all converted to EPW, there are some issues you should know • Breathing and bending mode theory has only been done in 1D
o Things could change if expanded to 3D
• Test-‐par6cles are massless, so no dynamical fric6on o If ini6al SagD mass heavy enough, it could affect orbit (Purcell et al. 2011)
• Galaxy could have been recently perturbed by an as yet uniden6fied dwarf o Chakrabar6 & Blitz (2009)
• Uncertainty in 6me and posi6on of last SagD pericentre o Could have been 0.8 – 1.1 Gyr ago, at distance of 15 – 20 kpc from Galac6c Centre
• Hyperbolic orbit approx. could overes6mate energy transfer to disc o D’Onghia et al. (2010) o Disc response and 6me dependence of encounter not taken into account
• We neglect spiral structure that would vary oscilla6on frequencies
What’s next?
• Dra{ submiUed to arXiv & MNRAS! Check out hUp://arxiv.org/abs/1507.07489 • If accepted, need to make changes according to referee • We’ll make our own changes in the meanwhile • Future simula6ons should take into account 6me dependence of encounter • Compare N-‐body and test-‐par6cle simula6ons for breathing/bending modes • Improved simula6ons and observa6ons could constrain SagD mass & orbit
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