J/ApJ/733/68ivo://CDS.VizieR/J/ApJ/733/68doi:10.26093/cds/vizier.17330068CDSBrown R.A.2022-05-05T10:40:48Z2012-12-07T15:05:53ZCDS support team

CDS, Observatoire de Strasbourg, 11 rue de l'Universite, F-67000 Strasbourg, France

cds-question@unistra.frsolar-system-planetsstellar-massesmultiple-starsExoplanet searches using radial velocity (RV) and microlensing (ML) produce samples of "projected" mass and orbital radius, respectively. We present a new method for estimating the probability density distribution (density) of the unprojected quantity from such samples. For a sample of n data values, the method involves solving n simultaneous linear equations to determine the weights of delta functions for the raw, unsmoothed density of the unprojected quantity that cause the associated cumulative distribution function (CDF) of the projected quantity to exactly reproduce the empirical CDF of the sample at the locations of the n data values. We smooth the raw density using nonparametric kernel density estimation with a normal kernel of bandwidth {sigma}. We calibrate the dependence of {sigma} on n by Monte Carlo experiments performed on samples drawn from a theoretical density, in which the integrated square error is minimized. We scale this calibration to the ranges of real RV samples using the Normal Reference Rule. The resolution and amplitude accuracy of the estimated density improve with n. For typical RV and ML samples, we expect the fractional noise at the PDF peak to be approximately 80n^-log2^. For illustrations, we apply the new method to 67 RV values given a similar treatment by Jorissen et al. (2001A&A...379..992J), and to the 308 RV values listed at exoplanets.org on 2010 October 20.2011ApJ...733...68Bhttps://cdsarc.cds.unistra.fr/viz-bin/cat/J/ApJ/733/68CatalogResearchIsServedByTAP VizieR generic serviceIsServedByConesearch servicerelated-toJ/A+A/527/A140 : Mass limits on substellar companions (Reffert+, 2011)http://exoplanets.org/ : Exoplanet orbit database web pagehttps://cds.unistra.fr/vizier-org/licences_vizier.htmlhttps://vizier.cds.unistra.fr/viz-bin/VizieR-2?-source=J/ApJ/733/68https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/ApJ/733/68http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/ApJ/733/68https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/ApJ/733/68https://vizier.iucaa.in/viz-bin/votable?-source=J/ApJ/733/68http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/ApJ/733/68GETtext/xml+votablehttps://tapvizier.cds.unistra.fr/TAPVizieR/tapCone search capability for table J/ApJ/733/68/table1 (The 308 values of msini from RV at exoplanets.org on 2010 October 20)https://vizier.cds.unistra.fr/viz-bin/conesearch/J/ApJ/733/68/table1?https://vizier.iucaa.in/viz-bin/conesearch/J/ApJ/733/68/table1?http://vizieridia.saao.ac.za/viz-bin/conesearch/J/ApJ/733/68/table1?GETtext/xml+votable180.050000true229.8617797-7.72227530.0055555555555555566/341 431 679 725 748 1597 2110 2152 2374 2416 2472 2497 3118 3536 3876 3932 3979 4136 4285 4429 4441 4444 4528 5009 5067 5309 5488 5522 5718 5815 6219 6760 6791 6821 6831 7136 7240 7746 7760 8357 8602 8843 9403 9459 9483 9662 9753 9843 9893 11087 11326 11352 11473 12030 12056 12465 12482 12502 12612 12644 12899 12983 13643 14275 14412 14416 14419 14434 14466 14525 14548 15174 15273 16035 16213 16627 16652 16707 16823 17266 17341 17496 17730-17731 17954 18028 18172 18441 18496 18614 18666 18821 18953 19904 19912 20072 20145 20557 20746 21003 21406 21838 21906 22036 22252 22590 22654 22878 23013 23030 23201 23363 23646 23681 24019 24178 24227 24924 25875 25939 26183 26242 26575 26706-26707 26790 26901 26978 26997 27018 27060 27088 27164 27616 27750 27881 27975 28044 28130 28548 28763 28767 28865 29291 29513 29541 30015 30170 30278 30419 30526 30541 30707 30770 31374 31494 31813 31860 32491 32509 32561 32848 32930 33243 33258 33377 33456 33630 33717 33813 33923 34069 34905 34951 35079 35362 35392 35442 35532 35907 35954 35968 36506 36697 37018 37461 37573 37954-37955 38545 38728 39257 39280 39364 39446 39591 39646 39926 40066 40101 40400 40442 40513 40692 40985 41167 41432 41446 41607 41724 42044 42248 42290 42318 42333 42386 42510 42570 42760 42934 43012 43228 43677 43813 43818 43911 44243 44379 44398 44740 44921 45168 45364 45624 45682 45717 45865 46111 46215 46297 46306 46632 46800 46843 46967 47550 47590 47930 48105 48108-48109 48519 48545https://cdsarc.cds.unistra.fr/viz-bin/moc/J/ApJ/733/68?format=asciidefaultJ/ApJ/733/68/table1The 308 values of msini from RV at exoplanets.org on 2010 October 20SimbadNameSimbad column added by the CDSmeta.idcharnullablerecnoRecord number assigned by the VizieR team. Should Not be used for identification.meta.recordintNameExoplanet namemeta.id;meta.maincharmsini[1.94/7730] Projected mass msin(i)(5.97236x10+24kg)phys.massdouble_RAPositions from SIMBAD database (right ascension part)degpos.eq.ra;meta.main_DEPositions from SIMBAD database (declination part)degpos.eq.dec;meta.main