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The above definitions ancl the ultrarelativistic hvdrodvnamic equations in planar geometry put the sonic point. (he point separating fluid elements which can communicate wilh the shock front via sound waves from those which cannot.at gy=4— 2/3. | The above definitions and the ultrarelativistic hydrodynamic equations in planar geometry put the sonic point, the point separating fluid elements which can communicate with the shock front via sound waves from those which cannot,at $g\chi=4-2\sqrt{3}$ . |
Requiring that the solutionpass smoothly through this point gives | Requiring that the solutionpass smoothly through this point gives |
nuages were retrieved frou the Spitzer archive for these objects. | images were retrieved from the Spitzer archive for these objects. |
The surface brightucss fitting was performed for these wnatclicd salaxies aud the objects satisfeiue ο>2” for three or more IRAC-bauds were retained for the FP analysis. | The surface brightness fitting was performed for these matched galaxies, and the objects satisfying $r_{e} > 2\,\arcsec$ for three or more IRAC-bands were retained for the FP analysis. |
We imposed this size limit iu order to work with a seuple with reliable à, values (see 33.0). | We imposed this size limit in order to work with a sample with reliable $r_{e}$ values (see 3.1). |
After removing ai few ealaxics (NCC1275, NGC(δι, NGCLITS. NCC6166) that show peculiar heht profiles GQuultiple source. close to a bright galaxy or stars). we finally identified 56 ealaxics with IRAC data in five clusters (A0126. A1656. A2199, A2631. and VIRGO) satistving our selection criteria. | After removing a few galaxies (NGC1275, NGC4824, NGC4478, NGC6166) that show peculiar light profiles (multiple source, close to a bright galaxy or stars), we finally identified 56 galaxies with IRAC data in five clusters (A0426, A1656, A2199, A2634, and VIRGO) satisfying our selection criteria. |
We prescut a bricf sumunary of the photometric information in Table L. | We present a brief summary of the photometric information in Table 1. |
The exposure times for the IRAC data range from 72 to 1000 sees. | The exposure times for the IRAC data range from 72 to 1000 secs. |
The above selection of the sample may introduce a bias in the derived FP. coefficieuts (Scodegeioctal. 1998)). | The above selection of the sample may introduce a bias in the derived FP coefficients \citealt{sco98}) ). |
However. such a bias would not affect our derivation of the wavelength dependence of the FP coefficients. since the nulti-vaveleusgth FP cocficients will be derived from the same galaxies for which the same bias would apply. | However, such a bias would not affect our derivation of the wavelength dependence of the FP coefficients, since the multi-wavelength FP coefficients will be derived from the same galaxies for which the same bias would apply. |
IRAF ELLIPSE was used to obtain surface brightuess profiles of our IRAC sample galaxies. | IRAF ELLIPSE was used to obtain surface brightness profiles of our IRAC sample galaxies. |
We restricted the fitting region to «>2 pixels (along the semiauajor axis} and discarded regions with S/N,,,, «1. | We restricted the fitting region to $a > 2\,$ pixels (along the semi-major axis) and discarded regions with $N_{rms}<\,$ 1. |
During the fit. we held the center. aud fixed the cllipticitics and the position angles of isophotes to those at the effective radius iu the 3.6 baud. | During the fit, we held the center, and fixed the ellipticities and the position angles of isophotes to those at the effective radius in the $\,\mu$ m band. |
In addition. 36 clipping was applied to reject outliersi such as foreeround stars. | In addition, $\,\sigma$ clipping was applied to reject outliers such as foreground stars. |
To subtract the background. we used the values determined from the SExtractor (Bertin&Arnouts1996). | To subtract the background, we used the values determined from the SExtractor \citep{ber96}. |
.. The adaptive backerouud mesh sizes were varied between 16 to ppixels. and the best mesh was chosen to be the one which flattened the growth curve at the largest isophote (a~3 Gua). | The adaptive background mesh sizes were varied between 16 to pixels, and the best mesh was chosen to be the one which flattened the growth curve at the largest isophote $a \sim\,$ $\,a_{e}$ ). |
After the ELLIPSE photometry, we used the de Vaucouleurs yl law to ft the observed surface brielituess profiles measured along the seumiaiuajor axis. | After the ELLIPSE photometry, we used the de Vaucouleurs $^{1/4}$ law to fit the observed surface brightness profiles measured along the semi-major . |
The fitting procedure vields the effective radius Gin “4 {ο"IUaja, Where a, is the effective seni major axis and (b/a), is the axis ratio of the isophote at this position. | The fitting procedure yields the effective radius (in $\arcsec$ ) $r_{e}=\sqrt{(b/a)_{e}}\,a_{e}$ where $a_{e}$ is the effective semi major axis and $(b/a)_{e}$ is the axis ratio of the isophote at this position. |
We tested the relability of our fitting procedure using the simulated. PSF-couvolved galaxies. and found that the surface brightness fitting gives unbiased. reliable results when r.>2”. | We tested the reliability of our fitting procedure using the simulated, PSF-convolved galaxies, and found that the surface brightness fitting gives unbiased, reliable results when $r_{e}
> 2\,\arcsec$ . |
At the same time. we ect the mean surface brightuess within r, (in ΕΜ Qe/=aye|x25log(arz)Di—E10log(1+BENERA(:) where myo is the maguitude of the total flix witlin the effective isophote defined by e, aud b5.. while cosmological dinuuing. galactic extinction (ely. using the formula of Laureijsetal.1996.. aud the extinction curve of Fitzpatrick&Massa.20073). and. I&-correction are taken iuto account. | At the same time, we get the mean surface brightness within $r_{e}$ (in AB magnitudes) $\langle\mu\rangle_{e} = m_{1/2} + 2.5\,\log\,(\pi r_{e}^2) - 10\,\log\,(1+z) -
A_{\lambda} - K(z)$ where $m_{1/2}$ is the magnitude of the total flux within the effective isophote defined by $a_{e}$ and $b_{e}$, while cosmological dimming, galactic extinction $A_{\lambda}$, using the formula of \citealt{lau94}, and the extinction curve of \citealt{fit07}) ), and K-correction are taken into account. |
The I&-correctiou is computed using the spectral energy distribution of a 136r age. solar moetalliitv. aud 0.1Cr burst model frou Diruzual&Charlot(2003).. assuming the Salpter initial uass function. | The K-correction is computed using the spectral energy distribution of a Gyr age, solar metallicity, and Gyr burst model from \citet{bru03}, assuming the Salpter initial mass function. |
The last observable. oy is a kinematic xuwanmeter and is nof expected to vary as a function of wavelength: we cousequenutlv use the same data used for he visible and NIR bauds (Pahlre1999). | The last observable, $\sigma_{0}$ is a kinematic parameter and is not expected to vary as a function of wavelength; we consequently use the same data used for the visible and NIR bands \citep{pah99}. |
. Iu our analvsis. augular sizes were converted iuto physical leneth units for the FP coustructiou by setting he distance to AL656 as MMpe aud calibrating the distances to individual clusters. utilizing the NIR FP (Pahreotal.LO98a) as a distance ladder. | In our analysis, angular sizes were converted into physical length units for the FP construction by setting the distance to A1656 as Mpc and calibrating the distances to individual clusters, utilizing the NIR FP \citep{pah98a} as a distance ladder. |
We fitted the FP coefficieuts of the inultivavebaud suuple iu the following iuanuucr usns a varietv of iiethlocdsa: where Gr). and (£j, are related as xX2.5log(Lj, | We fitted the FP coefficients of the multi-waveband sample in the following manner using a variety of methods: where $\langle \mu \rangle_{e}$ and $\langle I \rangle_{e}$ are related as $\langle \mu \rangle_{e}
\propto -2.5\,\log\,\langle I\rangle_{e}$. |
For the iuput r. aud (£j, we use ourGy, SB-fit results for AMR τὸν aud those listed iu Pabre(1999) for V- aud EI&-xuds. | For the input $r_{e}$ and $\langle I \rangle_{e}$, we use our SB-fit results for MIR 3.1), and those listed in \citet{pah99} for V- and K-bands. |
We tried five different fitting methods: standard cast-squares fit. the inverse least-squares fit. the bisector ofthe two. the least-squares fit to the orthogonal plauc. and the least absolute deviation fit to the orthogonal aue. | We tried five different fitting methods: standard least-squares fit, the inverse least-squares fit, the bisector of the two, the least-squares fit to the orthogonal plane, and the least absolute deviation fit to the orthogonal plane. |
These methods are outlined below. | These methods are outlined below. |
It is natmal to think of domme the standard least-squares fit of logà. (hereafter LSQ: Cuzimanetal.1993: Bernardietal. 2003)). but early FP work mainly took ogoy at the ordinate (Dressleretal.L987::; Djoreovski&Davis 1987:: hereafter inverse LSQ) for their purposes. | It is natural to think of doing the standard least-squares fit of $\log\,r_{e}$ (hereafter LSQ; \citealt{guz93}; \citealt{ber03}) ), but early FP work mainly took $\log\,\sigma_{0}$ at the ordinate \citealt{dre87}; \citealt{djo87}; hereafter inverse LSQ) for their purposes. |
More receut svork prefers the least-squares fittine of ogο by ninimuzues the variance orthogonal to the FP aue (hereafter orthogonal least-squares fit. or OLSQ: Bernardietal. 2003)) or the least absolute deviations orthogonal to the plane (hereafter orthogonal least absolute deviation fit. or OLAD: Jorgensenetal.1996:: DPahreetal. 1998a)). | More recent work prefers the least-squares fitting of $\log\,r_{e}$ by minimizing the variance orthogonal to the FP plane (hereafter orthogonal least-squares fit, or OLSQ; \citealt{ber03}) ) or the least absolute deviations orthogonal to the plane (hereafter orthogonal least absolute deviation fit, or OLAD; \citealt{jor96}; \citealt{pah98a}) ). |
The orthogonal fitting has au advantage over other methods. reducing the svstcmatic error by treating the variables sxauuuetricallv (Isobeotal. 1990). | The orthogonal fitting has an advantage over other methods, reducing the systematic error by treating the variables symmetrically \citep{iso90}. |
.. ILowever. the orthogonal methods vield larger nüieasurenmieut errors than the LSO wethods. especially for small samples (Isobeetal.1990). | However, the orthogonal methods yield larger measurement errors than the LSQ methods, especially for small samples \citep{iso90}. |
. Therefore. we also estimated the FP. coeficieuts by takine the bisector. or the plane equidistant from the planes obtained through the standard LSQ auc inverseLSQ (hereafter the LSQbisector). | Therefore, we also estimated the FP coefficients by taking the bisector, or the plane equidistant from the planes obtained through the standard LSQ and inverseLSQ (hereafter the LSQbisector). |
1.000. Monte Carlo saluplues of subsets of carly-type galaxies in Bernardi were performed to derive the FP cocfiicicut errors on a sample of 50 carly types to justify our approach. | 1,000 Monte Carlo samplings of subsets of early-type galaxies in \citet{ber03} were performed to derive the FP coefficient errors on a sample of 50 early types to justify our approach. |
Through the samplue. we fouud the errors | Through the sampling, we found the errors |
The images from the Mini-Mosaic. Camera have a much larger field of view than the IRTF data. | The images from the Mini-Mosaic Camera have a much larger field of view than the IRTF data. |
We trimmed and rotated each Game to match the NSFCaim field. | We trimmed and rotated each frame to match the NSFCam field. |
The relative photometry is based on the 7 magnitudes estimated for the M and L dwarf primaries from f—J colors given in Figure 4 of Dahnetal.(2002). | The relative photometry is based on the $I$ magnitudes estimated for the M and L dwarf primaries from $I-J$ colors given in Figure 4 of \citet{dahn}. |
. We estimated the J magnitudes because few of our targets have published photometry in the Z-band. | We estimated the $I$ magnitudes because few of our targets have published photometry in the $I$ -band. |
The relative photometry was measured in the same manner used for the NSFCam data (qphot). | The relative photometry was measured in the same manner used for the NSFCam data ). |
The candidate selection method was a nmmlti-step process. | The candidate selection method was a multi-step process. |
The initial stepused the Αι.)—IX color-magnitude cliagram. | The initial stepused the $M_{J}, J-K$ color-magnitude diagram. |
Figure G plots data for M. L. aud. T. dwarls with known trigonomeltric parallaxes. | Figure \ref{fig:sel} plots data for M, L, and T dwarfs with known trigonometric parallaxes. |
We have used those objects to delineate (he regions of the Aly.—IK plane where we would expect to find low-Iuminosityv companions to the ullracool targets. | We have used those objects to delineate the regions of the $M_{J}, J-K$ plane where we would expect to find low-luminosity companions to the ultracool targets. |
L dwarls have colors redder than JJ—A = 1. and are brighter than Mj~15.5: Classical T dwarls are bluer than JJ—A = 0.5 and [unter than M;=14: and transitional. earlv-tvpe T. dwarls have intermediate colors. aud 14<M,15.5. | L dwarfs have colors redder than $J-K$ = 1, and are brighter than $M_J \sim 15.5$; classical T dwarfs are bluer than $J-K$ = 0.5 and fainter than $M_J = 14$; and transitional, early-type T dwarfs have intermediate colors, and $14 < M_J < 15.5$. |
We identily candidate companions by plotting color-magnitude data lor each inlrared source as if il were al the same distance as the appropriate ullvacool target. | We identify candidate companions by plotting color-magnitude data for each infrared source as if it were at the same distance as the appropriate ultracool target. |
We use a Aly versus spectral (wpe relation to derive distances to all the target primaries that lack a trigonometric parallax. | We use a $M_J$ versus spectral type relation to derive distances to all the target primaries that lack a trigonometric parallax. |
This is (he vast majority of our sample. only 6/132 have (rigonometvic parallax measurements. | This is the vast majority of our sample, only 6/132 have trigonometric parallax measurements. |
The Cruzetal.(2003) relation has distances uncertainties of ~LO%. which corresponds to an uncertainty of +0.2 mag. | The \citet{kc03} relation has distances uncertainties of ${\sim}10\%$, which corresponds to an uncertainty of ${\sim}\pm0.2$ mag. |
If the source falls between (he dashed and dotted lines plotted in Figure 6.. then it is a potential low-luninosity companion. | If the source falls between the dashed and dotted lines plotted in Figure \ref{fig:sel}, then it is a potential low-luminosity companion. |
A total of 221 sources meet these criteria. | A total of 221 sources meet these criteria. |
Once the infrared. candidates are selected. we cross-reference each against5 the POSS and UST blue ancl red plates. as scanned in the Digital Skv Survey. 2003).. | Once the infrared candidates are selected, we cross-reference each against the POSS and UKST blue and red plates, as scanned in the Digital Sky Survey \citep{dposs}. |
These photographic5 plates have limiting5 magnitudes of D—22 and R21. while cool L and T dwarls have extremely. του optical-to-infrared. colors. (R-J)>6 1993). | These photographic plates have limiting magnitudes of $\sim$ 22 and $\sim$ 21, while cool L and T dwarfs have extremely red optical-to-infrared colors, $>$ 6 \citep{golim98}. |
. Thus. any sources visible on (he DSS scans can be ruled out as candidate companions. | Thus, any sources visible on the DSS scans can be ruled out as candidate companions. |
Thirty-six objects pass (is criterion. see Figure 6.. with colors consistent with late-L aud T cdwarfs. | Thirty-six objects pass this criterion, see Figure \ref{fig:sel}, , with colors consistent with late-L and T dwarfs. |
one each with 5 and 6. | one each with 5 and 6. |
Lissaner οἱ wusecl a variety of simple moclels for the distribution of the number of planets per svstem. | Lissauer et used a variety of simple models for the distribution of the number of planets per system. |
They. found that none of their models fit the data well. mostly because they produced too few svstems in which a single transiting planet was observed. but that the best-fit models twpically had mutual inclinations <5°, | They found that none of their models fit the data well, mostly because they produced too few systems in which a single transiting planet was observed, but that the best-fit models typically had mutual inclinations $\lesssim 5^\circ$. |
The purpose of this paper is to develop a general formalism (hat relates the intrinsic properties of multi-planet svstems to the properties of the mult-planet svstems that are detected in transit or other survevs relsec:survey and relsec:transil)). ancl to apply (iis formalism to the Kepler planet survey. relsec:kepler)) and to radial-velocitv surveys relsec:keprv)). | The purpose of this paper is to develop a general formalism that relates the intrinsic properties of multi-planet systems to the properties of the multi-planet systems that are detected in transit or other surveys \\ref{sec:survey} and \\ref{sec:transit}) ), and to apply this formalism to the Kepler planet survey \\ref{sec:kepler}) ) and to radial-velocity surveys \\ref{sec:keprv}) ). |
Previous analyses have used Monte Carlo simulations to explore (hese problems. but our ealeulations are mostly analviic or semi-analvtic and do not employ Monte Carlo methods. | Previous analyses have used Monte Carlo simulations to explore these problems, but our calculations are mostly analytic or semi-analytic and do not employ Monte Carlo methods. |
First we introduce some notation. ( | First we introduce some notation. ( |
i) The Kepler team uses (he term planet "eaucdidate" to denote a possible planet (hat has been discovered. through transits but not vet. been confirmed by racial-velocity measurements. | i) The Kepler team uses the term planet “candidate” to denote a possible planet that has been discovered through transits but not yet been confirmed by radial-velocity measurements. |
Morton&Johnson(2011) estimate that to of the IXepler planet candidates are real planets. so for the remainder of this paper we will simply assume that all (he Ixepler planet candidates are real and delete (he word "candidate". G | \cite{mor11} estimate that to of the Kepler planet candidates are real planets, so for the remainder of this paper we will simply assume that all the Kepler planet candidates are real and delete the word “candidate”. ( |
i) We must constantly disünguish between the number of planets in a svstem and the number of iransiting planets in that svstem. | ii) We must constantly distinguish between the number of planets in a system and the number of transiting planets in that system. |
We use the contraction "tranet (o denote "(ransiüng planet. | We use the contraction “tranet” to denote “transiting planet”. |
Thus one could have. for example. a (wo-lranel. three-planet svstem (Ragozzine&Iohan2010. call this a 7double-transitineg triple svstenr). ( | Thus one could have, for example, a two-tranet, three-planet system \citealt{rh10} call this a “double-transiting triple system”). ( |
ii) We disünguish two types of selection elfects that limit a planet sample. | iii) We distinguish two types of selection effects that limit a planet sample. |
Every. survey has a set ol detection thresholds. determined by (he parameters of the survey. that limit the properties of the planets (hat it can detect (maximum orbit period. minimun reflex radial velocity. minimum transit depth. ete). | Every survey has a set of detection thresholds, determined by the parameters of the survey, that limit the properties of the planets that it can detect (maximum orbit period, minimum reflex radial velocity, minimum transit depth, etc.). |
Asurvey selection effect is a limitation on (the number of detectable planets due to the detection thresholds. | A selection effect is a limitation on the number of detectable planets due to the detection thresholds. |
Ageometrical selection effect is a limitation arising from the orientation of the planetary svstemin particular. (he planet must cross in lront of the stellar disk to be detectable in a transit ν | A selection effect is a limitation arising from the orientation of the planetary system—in particular, the planet must cross in front of the stellar disk to be detectable in a transit . |
Ageometrical selection effect is a limitation arising from the orientation of the planetary svstemin particular. (he planet must cross in lront of the stellar disk to be detectable in a transit νο | A selection effect is a limitation arising from the orientation of the planetary system—in particular, the planet must cross in front of the stellar disk to be detectable in a transit . |
Ageometrical selection effect is a limitation arising from the orientation of the planetary svstemin particular. (he planet must cross in lront of the stellar disk to be detectable in a transit νον | A selection effect is a limitation arising from the orientation of the planetary system—in particular, the planet must cross in front of the stellar disk to be detectable in a transit . |
minimise real gradients. especially in zodiacal emission. | minimise real gradients, especially in zodiacal emission. |
The ollsct must however be sulliciently far from the galaxy that any real extended: emission associated with the galaxies halo does not appear simply às a zero olfset. | The offset must however be sufficiently far from the galaxy that any real extended emission associated with the galaxies' halo does not appear simply as a zero offset. |
The target choice. noted above. ensured these olfset conditions would be met by following cach primary exposure with a following Cconcatenated) exposure of a suitable background field. | The target choice, noted above, ensured these offset conditions would be met by following each primary exposure with a following (`concatenated') exposure of a suitable background field. |
The adopted field centres are listed in table 1 below. | The adopted field centres are listed in table 1 below. |
Thus each long integration for each field. consisted of 3360 separate short exposures. with elementary. integration time 2.]seconds. for a total on-target time of two hours per source. | Thus each long integration for each field consisted of 3360 separate short exposures, with elementary integration time 2.1seconds, for a total on-target time of two hours per source. |
The spacecraft was dithered by 2 areseconcs after every. 16 images. so that a given source fell at all points on a regular grid. covering 28 arcseconds. | The spacecraft was dithered by 2 arcseconds after every 16 images, so that a given source fell at all points on a regular grid covering $\times$ 28 arcseconds. |
Immediately. following cach source. an adjacent. partially overlapping where possible. olfset sskw area was observed in exactly the same way. | Immediately following each source, an adjacent, partially overlapping where possible, offset `sky' area was observed in exactly the same way. |
In this wav. in final processing. higher resolution can be recovered. while individual bad. pixels. and the biasing elfects of the row of pixels which is missing from the ISOCAM images. do not severely degrade the quality of the final result. | In this way, in final processing, higher resolution can be recovered, while individual bad pixels, and the biasing effects of the row of pixels which is missing from the ISOCAM images, do not severely degrade the quality of the final result. |
The standard [ISO pipeline reduction of the data uses the best available calibration files at the time of observation and the best available algorithms at the time of reduction. | The standard ISO pipeline reduction of the data uses the best available calibration files at the time of observation and the best available algorithms at the time of reduction. |
As is the case with other long-term projects. improved calibration files and more experience in data reduction continue to become available. so that the pipeline-processed. distributed data products do not correspond to the bestpossible reductions. | As is the case with other long-term projects, improved calibration files and more experience in data reduction continue to become available, so that the pipeline-processed distributed data products do not correspond to the bestpossible reductions. |
In order to benefit from the best available calibrations and algorithms. we have not utilised the standard ISO data products. but have reprocessed the raw data using the CAM Interactive Analysis (CLA)software. | In order to benefit from the best available calibrations and algorithms, we have not utilised the standard ISO data products, but have reprocessed the raw data using the CAM Interactive Analysis (CIA). |
The data. when converted to a useable format. are held as a cube. with the first two dimensions representing the individual images (210 per field in this case). and the third dimension representing the sequence of images taken. | The data, when converted to a useable format, are held as a cube, with the first two dimensions representing the individual images (210 per field in this case), and the third dimension representing the sequence of images taken. |
The reduction of the raw data requires the following steps. annotated below: | The reduction of the raw data requires the following steps, annotated below: |
Because the major methods ofdistance determination (Cepheids and TRGB) are calibrated to an LMC distance of 18.50 (50 kpe). it is here fixed at that distance.SAMC: | Because the major methods of distance determination (Cepheids and TRGB) are calibrated to an LMC distance of 18.50 (50 kpc), it is here fixed at that distance.: |
Neither of these has /Av-baud photometry. for reasons which are obvious on reflection. | Neither of these has $K$ -band photometry, for reasons which are obvious on reflection. |
Thev are in fact brighter (han most of the galaxies in the sample ancl so by rights should be included somehow. | They are in fact brighter than most of the galaxies in the sample and so by rights should be included somehow. |
But since thev are so close to the Milkv Wax. their A. luminosities do not allect anv caleulations separately from it; and their luminosities are almost certainly much smaller than theuncertainty in the Milky Way's. | But since they are so close to the Milky Way, their $K$ luminosities do not affect any calculations separately from it; and their luminosities are almost certainly much smaller than the in the Milky Way's. |
They. are therefore ignored in the A-band calculations.DPhoeni: | They are therefore ignored in the $K$ -band calculations.: |
There are (wo mutually incompatible optical radial velocity 1ieasurements for Phoenix. —52zc6 (Gallartetal...2001). and —1249 (Irwin&Tolstoy2002).. | There are two mutually incompatible optical radial velocity measurements for Phoenix, $-52 \pm 6$ \citep{GMG01} and $-13 \pm 9$ \citep{IT02a}. |
There is no obvious explanation for the difference between them. nor any clear reason to choose either. | There is no obvious explanation for the difference between them, nor any clear reason to choose either. |
I have (somewhat arbitrarily) used the latter.39032: | I have (somewhat arbitrarily) used the latter.: |
These had no listed radial velocity uncertaintv. and the original measurements could not be traced. | These had no listed radial velocity uncertainty, and the original measurements could not be traced. |
10 km ! is a conservative educated guess.Tucan: | 10 km $^{-1}$ is a conservative educated guess.: |
This also had no listed radial velocity uncertainty:the bins in the paper are 10 km ! wide. so this is a reasonable amount.Carina: | This also had no listed radial velocity uncertainty;the bins in the paper are 10 km $^{-1}$ wide, so this is a reasonable amount.: |
The listed photometry is taken from Materoetal.(1993).. and is based on mocdel-fitting.α | The listed photometry is taken from \citet{MOP93}, and is based on model-fitting.: |
ι The apparent magnitudes are back-caleulated. [rom the absolute magnitudes listed in suntzelfetal. (1992): the uncertainties are guesses. | The apparent magnitudes are back-calculated from the absolute magnitudes listed in \citet{SSO92}; the uncertainties are guesses. |
software aud SOIID package. | software and SQIID package. |
For the olajects. exposures of typically about 2 minutes (dithered iu short exposures of about 20s in J and 50s in IV. offset by about 2-3 arcsec) were taken ou the source aud ou the sky. uutil 16 total iuteeration time was achieved (see Table 2)). | For the objects, exposures of typically about 2 minutes (dithered in short exposures of about 20s in J and 50s in K' offset by about 2-3 arcsec) were taken on the source and on the sky, until the total integration time was achieved (see Table \ref{journal}) ). |
A necdian dark frame was calculated for every might with je same exposure time than that of the objects by using ie corresponding dark frames obtained before aud after ιο Observations. | A median dark frame was calculated for every night with the same exposure time than that of the objects by using the corresponding dark frames obtained before and after the observations. |
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