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<ri:Resource created="2018-11-20T15:22:06Z" status="active" updated="2025-05-19T09:50:00Z" version="1.2" xmlns:cs="http://www.ivoa.net/xml/ConeSearch/v1.0" xmlns:ri="http://www.ivoa.net/xml/RegistryInterface/v1.0" xmlns:vr="http://www.ivoa.net/xml/VOResource/v1.0" xmlns:vs="http://www.ivoa.net/xml/VODataService/v1.1" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.ivoa.net/xml/ConeSearch/v1.0 http://vo.ari.uni-heidelberg.de/docs/schemata/ConeSearch.xsd http://www.ivoa.net/xml/VOResource/v1.0 http://vo.ari.uni-heidelberg.de/docs/schemata/VOResource.xsd http://www.ivoa.net/xml/VODataService/v1.1 http://vo.ari.uni-heidelberg.de/docs/schemata/VODataService.xsd" xsi:type="vs:CatalogService"><title>Orbital parameters in Milky-Way-like potentials</title><shortName>I/348</shortName><identifier>ivo://CDS.VizieR/I/348</identifier><curation><publisher ivo-id="ivo://CDS">CDS</publisher><creator><name>Mackereth J.T.</name></creator><creator><name>Bovy J.</name></creator><date role="Updated">2019-01-07T08:49:30Z</date><date role="Created">2018-11-20T15:22:06Z</date><contact><name>CDS support team</name><address>CDS, Observatoire de Strasbourg, 11 rue de l'Universite, F-67000 Strasbourg, France</address><email>cds-question@unistra.fr</email></contact></curation><content><subject>milky-way-galaxy</subject><subject>stellar-populations</subject><subject>astrometry</subject><subject>astronomical-models</subject><description>Orbital parameters, such as eccentricity and maximum vertical excursion, of stars in the Milky Way are an important tool for understanding its dynamics and evolution, but calculation of such parameters usually relies on computationally-expensive numerical orbit integration. We present and test a fast method for estimating these parameters using an application of the Sackel fudge, used previously for the estimation of action-angle variables. We show that the method is highly accurate, to a level of &lt;1% in eccentricity, over a large range of relevant orbits and in different Milky Way-like potentials, and demonstrate its validity by estimating the eccentricity distribution of the RAVE-TGAS data set and comparing it to that from orbit integration. Using the method, the orbital characteristics of the ~7 million Gaia DR2 stars with radial velocity measurements are computed with Monte Carlo sampled errors in ~116 hours of parallelised cpu time, at a speed that we estimate to be ~3 to 4 orders of magnitude faster than using numerical orbit integration. We demonstrate using this catalogue that Gaia DR2 samples a large range of orbits in the solar vicinity, down to those with r_peri_&lt;~2.5kpc, and out to r_ap_&gt;~13kpc. We also show that many of the features present in orbital parameter space have a low mean zmax, suggesting that they likely result from disk dynamical effects.</description><source format="bibcode">2018PASP..130k4501M</source><referenceURL>https://cdsarc.cds.unistra.fr/viz-bin/cat/I/348</referenceURL><type>Catalog</type><contentLevel>Research</contentLevel><relationship><relationshipType>IsServedBy</relationshipType><relatedResource ivo-id="ivo://CDS.VizieR/TAP">TAP VizieR generic service</relatedResource></relationship><relationship><relationshipType>IsServedBy</relationshipType><relatedResource>Conesearch service</relatedResource></relationship><relationship><relationshipType>related-to</relationshipType><relatedResource ivo-id="ivo://CDS.VizieR/I/337">I/337 : Gaia DR1 (Gaia Collaboration, 2016)</relatedResource><relatedResource ivo-id="ivo://CDS.VizieR/I/345">I/345 : Gaia DR2 (Gaia Collaboration, 2018)</relatedResource></relationship></content><rights>https://cds.unistra.fr/vizier-org/licences_vizier.html</rights><capability><interface xsi:type="vr:WebBrowser"><accessURL use="full">https://vizier.cds.unistra.fr/viz-bin/VizieR-2?-source=I/348</accessURL><mirrorURL title="VizieR at IUCAA: Pune, India">https://vizier.iucaa.in/viz-bin/VizieR-2?-source=I/348</mirrorURL><mirrorURL title="VizieR at SAAO: SAAO, South Africa">http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=I/348</mirrorURL></interface></capability><capability><interface xsi:type="vs:ParamHTTP"><accessURL use="base">https://vizier.cds.unistra.fr/viz-bin/votable?-source=I/348</accessURL><mirrorURL title="VizieR at IUCAA: Pune, India">https://vizier.iucaa.in/viz-bin/votable?-source=I/348</mirrorURL><mirrorURL title="VizieR at SAAO: SAAO, South Africa">http://vizieridia.saao.ac.za/viz-bin/votable?-source=I/348</mirrorURL><queryType>GET</queryType><resultType>text/xml+votable</resultType></interface></capability><capability standardID="ivo://ivoa.net/std/TAP#aux"><interface xsi:type="vs:ParamHTTP" role="std"><accessURL use="base">https://tapvizier.cds.unistra.fr/TAPVizieR/tap</accessURL></interface></capability><capability xsi:type="cs:ConeSearch" standardID="ivo://ivoa.net/std/ConeSearch"><description>Cone search capability for table I/348/catalog (Catalog)</description><interface xsi:type="vs:ParamHTTP" role="std"><accessURL use="base">https://vizier.cds.unistra.fr/viz-bin/conesearch/I/348/catalog?</accessURL><mirrorURL title="VizieR at IUCAA: Pune, India">https://vizier.iucaa.in/viz-bin/conesearch/I/348/catalog?</mirrorURL><mirrorURL title="VizieR at SAAO: SAAO, South Africa">http://vizieridia.saao.ac.za/viz-bin/conesearch/I/348/catalog?</mirrorURL><queryType>GET</queryType><resultType>text/xml+votable</resultType></interface><maxSR>180.0</maxSR><maxRecords>50000</maxRecords><verbosity>true</verbosity><testQuery><ra>45.1321437478483</ra><dec>0.137850965984</dec><sr>0.005555555555555556</sr></testQuery></capability><coverage><spatial>0/0 1 2 3 4 5 6 7 8 9 10 11</spatial><footprint ivo-id="ivo://ivoa.net/std/moc">https://cdsarc.cds.unistra.fr/viz-bin/moc/I/348?format=ascii</footprint></coverage><tableset><schema><name>default</name><table><name>I/348/catalog</name><description>Catalog</description><column><name>JR</name><description>? Radial action (jr)</description><unit>kpc.km/s</unit><ucd>arith.grad;phys.veloc</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>recno</name><description>Record number assigned by the VizieR team. Should Not be used for identification.</description><ucd>meta.record</ucd><dataType xsi:type="vs:VOTableType">int</dataType></column><column><name>Source</name><description>Gaia DR2 source ID (source_id)</description><ucd>meta.id;meta.main</ucd></column><column><name>RA_ICRS</name><description>Gaia barycentric right ascension (ICRS) at Ep=2015.5 (ra)</description><unit>deg</unit><ucd>pos.eq.ra;meta.main</ucd><flag>indexed</flag></column><column><name>DE_ICRS</name><description>Gaia barycentric declination (ICRS) at Ep=2015.5 (dec)</description><unit>deg</unit><ucd>pos.eq.dec;meta.main</ucd><flag>indexed</flag></column><column><name>e</name><description>? Orbital eccentricity as defined in Equation (10) (e)</description><ucd>src.orbital.eccentricity</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>e_e</name><description>? rms uncertainty on e (e_err)</description><ucd>stat.error</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>zmax</name><description>? maximum vertical excursion from the midplane (zmax)</description><unit>kpc</unit><ucd>pos.cartesian.z;pos.galactic</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>n_zmax</name><description>[iI] i for -inf I for inf</description><ucd>meta.note</ucd><dataType xsi:type="vs:VOTableType" arraysize="1*">char</dataType></column><column><name>e_zmax</name><description>? rms uncertainty on zmax (zmax_err)</description><unit>kpc</unit><ucd>stat.error</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>rperi</name><description>? 3D pericenter radius (rperi)</description><unit>kpc</unit><ucd>phys.size.radius</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>n_rperi</name><description>[iI] i for -inf I for inf</description><ucd>meta.note</ucd><dataType xsi:type="vs:VOTableType" arraysize="1*">char</dataType></column><column><name>e_rperi</name><description>? rms uncertainty on rperi (rperi_err)</description><unit>kpc</unit><ucd>stat.error</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>rap</name><description>? 3D apocenter radius (rap)</description><unit>kpc</unit><ucd>phys.size.radius</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>n_rap</name><description>[iI] i for -inf I for inf</description><ucd>meta.note</ucd><dataType xsi:type="vs:VOTableType" arraysize="1*">char</dataType></column><column><name>e_rap</name><description>? rms uncertainty on rap (rap_err)</description><unit>kpc</unit><ucd>stat.error</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>ezmaxCor</name><description>? Correlation between e and zmax (e_zmax_corr) (1)</description><ucd>stat.correlation</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>erperiCor</name><description>? Correlation between e and rperi (e_rperi_corr) (1)</description><ucd>stat.correlation</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>erapCor</name><description>? Correlation between e and rap (e_rap_corr) (1)</description><ucd>stat.correlation</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>zmaxrperiCor</name><description>? Correlation between zmax and rperi (zmax_rperi_corr) (1)</description><ucd>stat.correlation</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>zmaxrapCor</name><description>? Correlation between zmax and rap (zmax_rap_corr) (1)</description><ucd>stat.correlation</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>rperirapCor</name><description>? Correlation between rperi and rap (rperi_rap_corr) (1)</description><ucd>stat.correlation</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>e_JR</name><description>? rms uncertainty on JR (jr_err)</description><unit>kpc.km/s</unit><ucd>stat.error</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>Lz</name><description>? 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Correlation between JR and LZ (jr_Lz_corr) (1)</description><ucd>stat.correlation</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>JRJZCor</name><description>? Correlation between JR and JZ (jr_jz_corr) (1)</description><ucd>stat.correlation</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>LZJZCor</name><description>? Correlation between LZ and JZ (lz_jz_corr) (1)</description><ucd>stat.correlation</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>omegaR</name><description>? 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Azimuthal frequency (omega_phi)</description><unit>Gyr**-1</unit><ucd>pos.ephem</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>e_omegaphi</name><description>? rms uncertainty on omegaphi (omega_phi_err)</description><unit>Gyr**-1</unit><ucd>stat.error</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>omegaz</name><description>? 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Radial angle (theta_r)</description><unit>rad</unit><ucd>pos.posAng</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>e_thetaR</name><description>? rms uncertainty on thetaR (theta_r_err)</description><unit>rad</unit><ucd>stat.error</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>thetaphi</name><description>? Azimuthal angle (theta_phi)</description><unit>rad</unit><ucd>pos.posAng</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>e_thetaphi</name><description>? rms uncertainty on thetaphi (theta_phi_err)</description><unit>rad</unit><ucd>stat.error</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>thetaz</name><description>? Vertical angle (theta_z)</description><unit>rad</unit><ucd>pos.posAng</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>e_thetaz</name><description>? rms uncertainty on thetaz (theta_z_err)</description><unit>rad</unit><ucd>stat.error</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>Rguide</name><description>? Radius of a circular orbit at the same Lz (rl)</description><unit>kpc</unit><ucd>phys.size.radius</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>e_Rguide</name><description>? rms uncertainty on Rguide (rl_err)</description><unit>kpc</unit><ucd>stat.error</ucd><dataType xsi:type="vs:VOTableType">double</dataType><flag>nullable</flag></column><column><name>E</name><description>? 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