Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator
X. Luri, M. Palmer, F. Arenou, E. Masana, J. de Bruijne, E. Antiche, C. Babusiaux, R. Borrachero, P. Sartoretti, F. Julbe, Y. Isasi, O. Martinez, A.C. Robin, C. Reylé, C. Jordi, J.M. Carrasco
AAstronomy & Astrophysics manuscript no. GOG23636 c (cid:13)
ESO 2014April 24, 2014
Overview and stellar statistics of the expected Gaia Catalogueusing the Gaia Object Generator
X. Luri , M. Palmer , F. Arenou , E. Masana , J. de Bruijne , E. Antiche , C. Babusiaux , R. Borrachero , P.Sartoretti , F. Julbe , Y. Isasi , O. Martinez , A.C. Robin , C. Reyl´e , C. Jordi , and J.M. Carrasco Dept. d’Astronomia i Meteorologia, Institut de Ci`encies del Cosmos, Universitat de Barcelona (IEEC-UB), Mart´ı Franqu`es 1,E08028 Barcelona, Spain. GEPI, Observatoire de Paris, CNRS, Universit´e Paris Diderot, 5 place Jules Janssen, 92190, Meudon, France Scientific Support O ffi ce of the Directorate of Science and Robotic Exploration of the European Space Agency, European SpaceResearch and Technology Centre, Keplerlaan 1, 2201 AZ, Noordwijk, The Netherlands Institut UTINAM, CNRS UMR 6213, Observatoire des Sciences de l’Univers THETA Franche-Comt´e-Bourgogne, Universit´e deFranche Comt´e, Observatoire de Besanc¸on, BP 1615, 25010 Besanc¸on Cedex, FrancePreprint online version: April 24, 2014
ABSTRACT
Aims.
An e ff ort has been made to simulate the expected Gaia Catalogue, including the e ff ect of observational errors. We statisticallyanalyse this simulated Gaia data to better understand what can be obtained from the Gaia astrometric mission. This catalogue is usedto investigate the potential yield in astrometric, photometric, and spectroscopic information and the extent and e ff ect of observationalerrors on the true Gaia Catalogue. This article is a follow-up to Robin et al. (A&A 543, A100, 2012), where the expected GaiaCatalogue content was reviewed but without the simulation of observational errors. Methods.
We analysed the Gaia Object Generator (GOG) catalogue using the Gaia Analysis Tool (GAT), thereby producing a numberof statistics about the catalogue.
Results.
A simulated catalogue of one billion objects is presented, with detailed information on the 523 million individual singlestars it contains. Detailed information is provided for the expected errors in parallax, position, proper motion, radial velocity, and thephotometry in the four Gaia bands and for the physical parameter determination including temperature, metallicity, and line of sightextinction.
Key words.
Stars: statistics – Galaxies: statistics – Galaxy: stellar content – Methods: data analysis – Astrometry – Catalogues
1. Introduction
Gaia, a cornerstone ESA mission, launched in December 2013,will produce the fullest 3D galactic census to date, and it is ex-pected to yield a huge advancement in our understanding of thecomposition, structure, and evolution of the Galaxy (Perrymanet al. 2001). Through Gaia’s photometric instruments, object de-tection up to G =
20 mag will be possible (see Jordi et al. (2010)for a definition of G magnitude), including measurements of po-sitions, proper motions, and parallaxes up to micro arcsecondaccuracy. The on-board radial velocity spectrometer will pro-vide radial velocity measurements for stars down to a limit of G RVS =
17 mag. With low-resolution spectra providing infor-mation on e ff ective temperature, line of sight extinction, surfacegravity, and chemical composition, Gaia will yield a detailed cat-alogue that contains roughly 1% of the entire galactic stellar pop-ulation.Gaia will represent a huge advance on its predecessor,Hipparcos (Perryman & ESA 1997), both in terms of massiveincreases in precision and in the numbers of objects observed.Thanks to accurate observations of large numbers of stars ofall kinds, including rare objects, large numbers of Cepheids andother variable stars, and direct parallax measurements for starsin all galactic populations (thin disk, thick disk, halo, and bulge),Gaia data is expected to have a strong impact on luminosity cal-ibration and improvement of the distance scale. This, along withapplications to studies of galactic dynamics and evolution and of fields ranging from exoplanets to general relativity and cosmol-ogy, Gaia’s impact is expected to be significant and far reaching.During its five years of data collection, Gaia is expected totransmit some 150 terabytes of raw data to Earth, leading to pro-duction of a catalogue of 10 individual objects. After on-groundprocessing, the full database is expected to be in the range ofone to two petabytes of data. Preparation for acquiring this hugeamount of data is essential. Work has begun to model the ex-pected output of Gaia in order to predict the content of the GaiaCatalogue, to facilitate the production of tools required to e ff ec-tively validate the real data before publication, and to analyse thereal data set at the end of the mission.To this end, the Gaia Data Processing and AnalysisConsortium (DPAC) has been preparing a set of simulators, in-cluding a simulator called the Gaia Object Generator (GOG),which simulates the end-of-mission catalogue, including obser-vational errors. Here a full description of GOG is provided, in-cluding the models assumed for the performance of the Gaiasatellite and an overview of its simulated end-of-mission cata-logue. A selection of statistics from this catalogue is provided togive an idea of the performance and output of Gaia.In Sect. 2, a brief description of the Gaia instrument andan overview of the current simulation e ff ort is given, followedby definitions of the error models assumed for the performanceof the Gaia satellite in Sec. 3. In Sec. 4, the methods used forsearching the simulated catalogue and generating statistics are a r X i v : . [ a s t r o - ph . I M ] A p r . Luri et al.: Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator described. In Sec. 5, we present the results of the full sky sim-ulation, broken up into sections for each parameter in the cata-logue and specific object types of interest. Finally, in Sec. 6 weprovide a summery and conclusions.
2. The Gaia satellite
The Gaia space astrometry mission will map the entire sky in thevisible G band over the course of its five-year mission. Locatedat Lagrangian point L2, Gaia will be constantly and smoothlyspinning. It has two telescopes separated by a basic angle of106 . ◦ . Light from stars that are observed in either telescope iscollected and reflected to transit across the Gaia focal plane.The Gaia focal plane can be split into several main compo-nents. The majority of the area is taken up by CCDs for the broadband G magnitude measurements in white light, used in takingthe astrometry measurements. Second, there is a pair of low-resolution spectral photometers, one red and one blue, produc-ing low-resolution spectra with integrated magnitude G RP and G BP , respectively. Finally, there is a radial velocity spectrome-ter observing at near-infrared, with integrated magnitude G RVS .The magnitudes G , G RP , and G BP will be measured for all Gaiasources ( G ≤ G RVS will be measured for objectsup to G RVS ≤
17 magnitude. For an exact definition of the Gaiafocal plane and the four Gaia bands, see Figs. 1 and 3 of Jordiet al. (2010).The motion of Gaia is complex, with rotations on its ownspin axis occurring every six hours. This spin axis is itself pre-cessing, and is held at a constant 45 ◦ degrees from the Sun. Fromits position at L2, Gaia will orbit the Sun over the course of ayear. Thanks to the combination of these rotations, the entiresky will be observed repeatedly. The Gaia scanning law givesthe number of times a region will be re-observed by Gaia overits five-year mission, and comes from this spinning motion ofthe satellite and its orbit around the Sun. Objects in regionswith more observations have greater precision, while regionswith fewer repeat observations have lower precision. The aver-age number of observations per object is 70, although it can beas low as a few tens or as high as 200.
3. Simulations
Simulation of many aspects of the Gaia mission has been carriedout in order to test and improve instrument design, data reductionalgorithms, and tools for using the final Gaia Catalogue data. TheGaia Simulator is a collection of three data generators designedfor this task: the Gaia Instrument and Basic Image Simulator(GIBIS, Babusiaux 2005), the Gaia System Simulator (GASS,Masana et al. 2010), and the Gaia Object Generator (GOG, de-scribed here). Through these three packages, the production ofthe simulated Gaia telemetry stream, observation images downto pixel level and intermediate or final catalogue data is possible.
One basic component of the Gaia Simulator is its UniverseModel (UM), which is used to create object catalogues down to aparticular limiting magnitude (in our case G =
20 mag for Gaia).For stellar sources, the UM is based on the Besanc¸on galaxymodel (Robin et al. 2003). This model simulates the stellar con-tent of the Galaxy, including stellar distribution and a numberof object properties. It produces stellar objects based on the four main stellar populations (thin disk, thick disk, halo, and bulge),each population with its own star formation history and stellarevolutionary models. Additionally, a number of object-specificproperties are also assigned to each object, dependent on its type.Possible objects are stars (single and multiple), nebulae, stellarclusters, di ff use light, planets, satellites, asteroids, comets, re-solved galaxies, unresolved extended galaxies, quasars, AGN,and supernovae. Therefore, the UM is capable of simulating al-most every object type that Gaia can potentially observe. It cantherefore construct simulated object catalogues down to Gaia’slimiting magnitude.Building on this, the UM creates for any time, over any sec-tion of the sky (or the whole sky), a set of objects with positionsand assigns each a set of observational properties (Robin et al.2012). These properties include distances, apparent magnitudes,spectral characteristics, and kinematics.Clearly the models and probability distributions used in or-der to create the objects with their positions and properties arehighly important in producing a realistic catalogue. The UM hasbeen designed so that the objects it creates fit as closely as pos-sible to observed statistics and to the latest theoretical formationand evolution models (Robin et al. 2003). For a statistical anal-ysis of the underlying potentially observable population (with G ≤
20 mag) using the Gaia UM without satellite instrumentspecifications and error models, see Robin et al. (2012).
The GOG is capable of transforming this UM catalogue intoGaia’s simulated intermediate and final catalogue data. This isachieved through the use of analytical and numerical error mod-els to create realistic observational errors in astrometric, photo-metric, and spectroscopic parameters (Isasi et al. 2010). In thisway, GOG transforms ‘true’ object properties from the UM into‘observed’ quantities that have an associated error that dependson the object’s properties, Gaia’s instrument capabilities, and thetype and number of observations made.
DPAC is divided into a number of coordination units (CUs), eachof which specialises in a specific area. In GOG we have takenthe recommendations from the various CUs in order to includethe most complete picture of Gaia performance as possible. TheCUs are divided into the following areas: CU1, system archi-tecture; CU2, simulations; CU3, core processing (astrometry);CU4, object processing (multiple stars, exoplanets, solar systemobjects, extended objects); CU5, photometric processing; CU6,spectroscopic processing; CU7, variability processing; CU8, as-trophysical parameters; and CU9, catalogue access.Models for specific parameters have been provided by thevarious CUs, and only an outline is given here. In the follow-ing description, true refers to UM data (without errors), epoch to simulated individual observations (including errors), and ob-served to the simulated observed data for the end of the Gaiamission (including standard errors). Throughout, error refers tothe formal standard error on a measurement.
2. Luri et al.: Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator
The formal error on the parallax, σ (cid:36) , is calculated following theexpression: σ (cid:36) = m · g (cid:36) · (cid:115) σ η N e ff + σ N transit (1) – σ η is the CCD centroid positioning error. It uses the CramerRao (CR) lower bound in its discrete form, which definesthe best possible precision of the maximum likelihood cen-troid location estimator. The CR lower bound requires theline spread function (LSF) derivative for each sample , thebackground, the readout noise, and the source integrated sig-nal. – m is the contingency margin that is used to take scientificand environmental e ff ects into account, for example: uncer-tainties in the on-ground processing, such as uncertainties inrelativistic corrections and solar system ephemeris; e ff ectssuch as having an imperfect calibrating LSF; errors in esti-mating the sky background; and other e ff ects when dealingwith real stars. The default value assumed for the Gaia mis-sion has been set by ESA as 1.2 and is used in GOG. – g (cid:36) = . / sin ξ is a geometrical factor where ξ is known asthe solar aspect angle, with a value of 45 ◦ . – N e ff is the number of elementary CCD transits ( N strip × N transit ). – N transit is the number of field of view transits. – N strip is the number of CCDs in a row on the Gaia focal plane.It has a value of 9, except for the row that includes the wave-front sensor, which has 8 CCDs. – σ cal is the calibration noise. A constant value of 5.7 µ as hasbeen applied. This takes into account that the end-of-missionprecision on the astrometric parameters not only dependson the error due to the location estimation with each CCD.There are calibration errors from the CCD calibrations, theuncertainty of the attitude of the satellite and the uncertaintyon the basic angle.We are enabling the activation of gates, as described in theGaia Parameter Database. The Gaia satellite will be smoothlyrotating and will constantly image the sky by collecting the pho-tons from each source as they pass along the focal plane. Thetotal time for a source to pass along the focal plane will be 107seconds, and the electrons accumulated in the a CCD pixel willbe passed along the CCD at the same rate as the source. To avoidsaturation for brighter sources, and the resulting loss of astro-metric precision, gates can be activated that limit the exposuretime. Here we are using the default gating system, which couldchange during the mission.Following de Bruijne (2012) (see alsohttp: // / web / gaia / science-performance),we have assumed that the errors on the positional coordinatesat the mean epoch (middle of the mission), and the error in theproper motion coordinates can be given respectively by – σ α = . σ (cid:36) – σ δ = . σ (cid:36) – σ µ α = . σ (cid:36) – σ µ δ = . σ (cid:36) In Gaia, a sample is defined as a set of individual pixels.
GOG uses the single CCD transit photometry error σ p,j (Jordiet al. 2010) defined as σ p,j [mag] = . · log ( e ) · (cid:113) f aperture · s j + ( b j + r ) · n s · (1 + n s n b ) f aperture · s j (2)to compute either the epoch errors or the end-of-mission errors.We assume, following an ‘aperture photometry’ approach,that the object flux s j is measured in a rectangular ‘aperture’(window) of n s along-scan object samples. The sky background b j is assumed to be measured in n b background samples, and r is CCD readout noise. The f aperture · s j is expressed in units ofphoto-electrons ( e − ), and denotes the object flux in photometricband j contained in the ‘aperture’ (window) of n s samples, aftera CCD crossing. The number f aperture thus represents the fractionof the object flux measured in the aperture window.For the epoch and end-of-mission data, the same expressionis used for the standard deviation calculation σ G,j = m · (cid:115) σ + σ N e ff (3)where N e ff is the number of elementary CCD transits ( N strip × N transit ), with ( N strip = N transit ) = σ cal has a fixed value of σ cal = CU6 tables (see Table 1) using the stars’ physical parametersand apparent magnitude are used to obtain σ V r . They were com-puted following the prescriptions of Katz et al. (2004) and laterupdates. Those tables have been provided for one and 40 field-of-view transits, therefore the value for 40 transits is used hereto calculate the average end-of-mission errors in RVS.Given the information on the apparent Johnson V magnitudeand the atmospheric parameters of each star (from the UM),we select from Table 1 the closest spectral type and return thecorresponding radial velocity error. Since Table 1 is given for[Fe / H] = ff erent metallicities into account: for eachvariation in metallicity of ∆ [Fe / H] = V = · s − . Forthe faintest stars the spectra will be of poor quality and will notcontain enough information to enable accurate estimation of theradial velocity. Owing to the limited bandwidth in the downlinkof Gaia data to Earth, poor quality spectra will not be transmit-ted. We therefore set an upper limit on the radial velocity error of20 km · s − , beyond which we assume that there will be no data.The exact point at which the data will be assumed to have toolow a quality is still unknown. GOG uses the stellar parametrisation performance given by CU8to calculate error estimations for e ff ective temperature, line-of-sight extinction, metallicity, and surface gravity. The colour-independent extinction parameter A is used in preference to the
3. Luri et al.: Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator (cid:80)(cid:80)(cid:80)(cid:80)(cid:80)(cid:80)
Type V Table 1.
The average end-of-mission formal error in radial velocity with an assumed average of 40 field-of-view transits, in km · s − ,for each spectral type. The numbers in the top row are Johnson apparent V magnitudes. Fields marked by “n” are assumed to betoo faint to produce spectra with su ffi cient quality for radial velocity determination. Stars with these magnitudes will have no radialvelocity information.band specific extinctions A V or A G , because A is a propertyof the interstellar medium alone (Bailer-Jones 2011). CU8 usethree di ff erent algorithms to calculate physical parameters usingspectrophotometry (see Liu et al. (2012)).It should be noted that the errors calculated here are calcu-lated only as a function of apparent magnitude. However, as de-scribed in Liu et al. (2012), there are clear dependencies on thespectral type of the star, because some star types may or maynot exhibit spectral features required for parameter determina-tion. Additionally, Liu et al. (2012) report a strong correlationbetween the estimation of e ff ective temperature and extinction.This correlation is not simulated in GOG. Following the recom-mendation of CU8, calculating errors of physical parameters de-pends on apparent magnitude and is split into two cases, objectswith A < A ≥ σ T e ff , σ A , σ Fe / H and σ log g are calculated from aGamma distribution, with shape parameter α and scale parame-ter θ : f ( σ ; α, θ ) = Γ ( σ ) θ α σ α − e − x θ (4)where α and θ are obtained from the following expressions,which have been calculated to give each σ a close approxima-tion to the CU8 algorithm results. A gamma distribution wasselected for ease of implementation and for its ability to statis-tically recreate the CU8 results to a reasonable approximation.A gamma distribution is also only non-zero for positive valuesof sigma. This is essential when modelling errors because, ofcourse, it is impossible to have a negative error. – For stars with A < α A = . − . G + . G α log g = . − . G + . G α Fe / H = . − . G + . G α T e ff = . − . G + . G θ A = . θ log g = . θ Fe / H = . θ T e ff = . . – For stars with A ≥ α A = . − . G + . G α log g = . − . G + . G α Fe / H = . − . G + . G α T e ff = . − . G + . G θ A = . θ log g = . θ Fe / H = . θ T e ff = . . The Gamma distributions thus obtained for each parameterare used to generate a formal error for each parameter for eachindividual star, aiming to statistically (but not individually) re-produce the results that will be obtained by the application ofthe CU8 algorithms and then included in the Gaia Catalogue.It should be noted that in the stellar parametrisation algo-rithms used in Liu et al. (2012), a degeneracy is reported be-tween extinction and e ff ective temperature owing to the lack ofresolved spectral lines only sensitive to e ff ective temperature. InGOG, this degeneracy has not been taken into account, and theprecisions of each of the four stellar parameters is simulated in-dependently.Additionally, the results of Liu et al. (2012) have recentlybeen updated, and Bailer-Jones et al. (2013) gives the latest re-sults regarding the capabilities of physical parameter determi-nation. This latest paper has not been included in the currentversion of GOG. In the present paper, only the results for single stars are givenin detail. All of the figures and tables represent the numbers andstatistics of only individual single stars, excluding all binary andmultiple systems. Since the performance of the Gaia satellite islargely unknown for binary and multiple systems, the implemen-tation into GOG of realistic error models has not yet been possi-ble. While the results presented in Sec. 5 are expected to be reli-able under current assumptions for the performance of Gaia, the
4. Luri et al.: Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator real Gaia Catalogue will di ff er from these results thanks to thepresence of binary and multiple systems. By removing binariesfrom the latter, direct comparison of the results presented herewith the real Gaia Catalogue will not be possible because of thepresence of unresolved binaries, which are di ffi cult to detect. Asa simulator, GOG relies heavily on all inputs and assumptionssupplied both from the UM or from the Gaia predicted perfor-mance and error models.In our simulations we used an exact cut at G =
20 mag,beyond which no stars are observed. In reality, in regions of lowdensity observations of stars up to 20.5 mag could be possible.Inversely, very crowded regions may not be complete up to 20mag, or the numbers of observations per star over the five-yearmission may be reduced in these regions.There is no simulation of the impact of crowding on objectdetection or the detection of components in binary and multiplesystems. This can lead to unrealistic quality in all observed datain the most crowded regions of the plane of the Galaxy, to over-estimates for star counts in the bulge, and to a lack of featuresrelated to the disk and bulge in Figs. 3 and 19.Additionally, GOG uses the nominal Gaia scanning law tocalculate the number of field of view transits per object over thefive years of the mission while Gaia is operating in normal mode.There will be an additional one-month period at the start of themission using an ecliptic pole scanning law, and this has not beentaken into account. It may lead to a slight underestimation ofthe number of transits, and therefore a slight overestimation oferrors, for some stars near the ecliptic poles.There is the possibility that the Gaia mission will be ex-tended above the nominal five-year mission. Since this ideais under discussion and has not yet been confirmed or dis-carded, we only present results for the Gaia mission as originallyplanned.If the length of the mission is increased, the number of field-of-view transits will increase, and the precision per object willimprove. If the proposal is accepted, the GOG simulator couldbe used to provide updated statistics for the expected cataloguewithout extensive modification.
4. Methods and statistics
Considering current computing capabilities, it is not straightfor-ward to make statistics and visualisations when dealing with cat-alogues of such a large size. A specific tool has been createdwhich is capable of extracting information and visualising re-sults, with excellent scalability allowing its use for huge datasetsand distributed computing systems.The Gaia Analysis Tool (GAT) is a data analysis packagethat allows, through three distinct frameworks, generation ofstatistics, validation of data, and generation of catalogues. It cur-rently handles both UM- and GOG-generated data, and could beadapted to handle other data types.Every statistical analysis is performed by a StatisticalAnalysis Module (SAM), with several grouped into a singleXML file as an input to GAT. Each SAM can contain a set of fil-ters, enabling analysis of specific subsets of the data. This allowsthe production of a wide range of statistics for objects satisfyingany number of specific user-defined criteria or for the catalogueas a whole.GAT creates a number of di ff erent statistics outputs includ-ing histograms, sky density maps and HR diagrams. After theGAT execution, statistics output are stored to either generate areport or to be analysed using the GAT Displaying tool. Because we have information from not only observations ofa population but also of the observed population itself, compar-ison is possible between the simulated Gaia Catalogue and thesimulated ‘true’ population, allowing large scope for investigat-ing the precision of the observations and di ff erences betweenthe two catalogues. Clearly this is only possible with simulateddata and cannot be attempted with the true Gaia Catalogue, soit is an e ff ective way to investigate the possible extent and ef-fect of observational errors and selection bias on the real GaiaCatalogue, where this kind of comparison is not possible.GOG can be used in the preparations for validating the trueGaia Catalogue, by testing the GOG catalogue for accuracy andprecision. In special cases, observational biases could even beimplemented into the code to allow thorough testing of valida-tion methods.
5. Results
The GOG simulator has been used to generate the simulated fi-nal mission catalogue for Gaia, down to magnitude G =
20. Thesimulation was performed on the MareNostrum super computerat the Barcelona Supercomputing Centre (Centre Nacional deSupercomputaci´o), and it took 400 thousand CPU hours. An ex-tensive set of validations and statistics have been produced usingGAT to validate performance of the simulator. Below we includea subset of these statistics for the most interesting cases to givean overview of the expected Gaia Catalogue.
In total, GOG has produced a catalogue of about one billion ob-jects, consisting of 523 million individual single stars and 484million binary or multiple systems. The total number of stars,including the components of binary and multiple systems is 1.6billion. The skymap of the total flux detected over the entire five-year mission is given in Fig. 1. Although GOG can produce ex-tragalactic sources, none have been simulated here.The following discussion is split into sections for di ff erenttypes of objects of interest. Section 5.2 covers all galactic stellarsources. Section 5.3 covers all variable objects. Section 5.4 is adiscussion of physical parameters estimated by Gaia. All objectsin these sections are within the Milky Way.To make the presentation of performance as clear as possible,all binary and multiple systems and their components have beenremoved from the following statistics. This is due to complicat-ing e ff ects that arise when dealing with binary systems, someof which GOG is not yet capable of correctly simulating; forexample, GOG does not yet contain an orbital solution in its as-trometric error models, and the e ff ects of unresolved systemson photometry and astrophysical parameter determination havenot yet been well determined. Therefore, the numbers presentedare only for individual single stars and do not include the fullone billion objects simulated. Of the single stars presented inthis paper, 74 million are within the radial velocity spectrometermagnitude range.Table 2 gives the mean and median error for each of the ob-served parameters discussed in this paper, along with the upperand lower 25% quartile. Here we assume the standard definition of accuracy and precision:accuracy is the closeness of a result (or set) to the actual value, i.e. it isa measure of systematics or bias. Precision is the extent of the randomvariability of the measurement, i.e. what is called observational errorsabove. 5. Luri et al.: Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator
Fig. 1.
Skymap of total integrated flux over the Milky Way, in the G band. The colour bar represents a relative scale, from maximumflux in white to minimum flux in black. The figure is plotted in galactic coordinates with the galactic-longitude orientation swappedleft to right.In Fig. 2, the mean error for parallax, position, proper mo-tion, and photometry in the four Gaia bands are given as a func-tion of G magnitude. Also, the mean error in radial velocity isgiven as a function of G RVS magnitude. The sharp jumps in themean error in astrometric parameters between 8 and 12 mag aredue to the activation of gates for the brighter sources in an at-tempt to prevent CCD saturation (see Sec. 3.3.1).
The distribution of parallax measurements for all single stars isgiven in Fig. 4. The mean parallax error for all single stars is147.0 µ as. The number of single stars falling below three rela-tive parallax error limits is given in Table 3 for each spectral typeand in Table 4 for each luminosity class. For those interested ina specific type of star, Table 5 gives the full breakdown of thenumber of single stars falling below three relative parallax errorlimits for every spectral type and luminosity class. The distribu-tion of parallax errors is given for each stellar population in Fig.5 and for each spectral type in Fig. 7. The relative parallax error σ (cid:36) /(cid:36) is given in Fig. 6 for stars split by spectral type.The error in parallax measurements for Gaia depends on themagnitude of the source, the number of observations made, andthe true value of the parallax. Figure 3 shows the mean paral-lax error over the sky. Its shape clearly follows that of the Gaiascanning law. The red area corresponding to the region of worstprecision is due to the bulge population, which su ff ers from highlevels of reddening. The faint ring around the centre of the figurecorresponds to the disk of the Galaxy, remembering that the plot Standard error LQ Median Mean UQParallax ( µ as) 80 140 147 210 α ∗ ( µ as) 40 80 91 130 δ ( µ as) 50 100 103 150 µ α ( µ as · yr − ) 40 80 82 120 µ δ ( µ as · yr − ) 40 70 73 110 G (mmag) 2 3 3.0 4 G BP (mmag) 6 11 14.6 19 G RP (mmag) 5 7 7.7 10 G RVS (mmag) 6 11 13.2 18Radial velocity (km · s − ) 3 7 8.0 13Extinction (mag) 0.16 0.21 0.21 0.26Metallicity (Fe / H) 0.46 0.57 0.57 0.73Surface gravity (log g ) 0.34 0.35 0.45 0.58E ff ective temperature (K) 280 350 388 530 Table 2.
Mean and median value of the end-of-mission error ineach observable, along with the upper (UQ) and lower (LQ) 25%quartile. Since the error distributions are not symmetrical, themean value should not be used directly, and is given only to givean idea of the approximate level of Gaia’s precision. The median G magnitude of all single stars is 18.9 mag.is given in equatorial coordinates. The blue areas correspondingto regions of improved mean precision are areas with a highernumber of observations. The characteristic shape of this plot isdue to the Gaia scanning law. The error in parallax as a function
6. Luri et al.: Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator
G magnitude [mag] M e a n e rr o r [ µ a s ] $αδ G magnitude [mag] M e a n e rr o r [ µ a s y r − ] µ α µ δ G magnitude [mag] M e a n e rr o r [ mm ag ] GGBPGRPGRVS G RVS magnitude [ mag ] M e a n e rr o r [ k m s − ] Radial velocity
Fig. 2.
Mean end-of-mission error as a function of G magnitude for parallax, position, proper motion, and photometry in the fourGaia passbands. Additionally the mean end-of-mission error in radial velocity as a function of G RVS magnitude.
Spec. type Total σ (cid:36) /(cid:36) < σ (cid:36) /(cid:36) < . σ (cid:36) /(cid:36) < .
05O 3.3 × × × × × × × Table 3.
Total number of single star for each spectral type, alongwith the percentage of those that fall below each relative parallaxerror limit; e.g., 68% of M-type stars have a relative parallaxerror better than 20%.of measured G magnitude is given in Fig. 8 and as a function ofthe real parallax in Fig. 9. Gaia will be capable of measuring the position of each observedstar at an unprecedented accuracy, producing the most precisefull sky position catalogue to date.
Lum. class Total σ (cid:36) /(cid:36) < σ (cid:36) /(cid:36) < . σ (cid:36) /(cid:36) < . . × . × . × . × . × . × Table 4.
Total number of single stars for each luminosity class,along with the percentage that fall below each relative parallaxerror limit.The mean error is 90 µ as for right ascension and 103 µ as fordeclination. The distribution of error in right ascension and dec-lination as a function of the true value, along with a histogramof the error, are given in Figs. 10 and 11. The overdensities aredue to the bulge of the Galaxy. In addition to parallax measurements, Gaia will also measureproper motions for all stars it detects. The proper motion in rightascension and declination is labelled as µ α and µ δ , respectively.
7. Luri et al.: Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator − Parallax [ µ as] C o un t All stars
Fig. 4.
Histogram of parallax for all single stars. The his-togram contains 99.5% of all data.
Error in Parallax [ µ as] C o un t AllThin DiskThick DiskHaloBulge
Fig. 5.
Histogram of end-of-mission parallax error for allsingle stars, split by stellar population. . . . . . . Relative error in Parallax [ σ $ /$ ] C u m u l a t i v e C o un t AllO typeB typeA typeF typeG typeK typeM typeWhite Dwarf
Fig. 6.
Cumulative histogram of relative parallax error forall single stars, split by spectral type. The histogram rangedisplays 74% of all data.
Parallax Error [ µ as] C o un t AllO typeB typeA typeF typeG typeK typeM typeWhite Dwarf
Fig. 7.
Histogram of end-of-mission parallax error for allsingle stars, split by spectral type.
Fig. 3.
Sky map (healpix) of mean parallax error for all singlestars in equatorial coordinates. Colour scale is mean parallax er-ror in µ as. The red area is the location of the bulge. The mean error in µ α is 81.7 µ as · yr − , and in µ δ is 72.9 µ as · yr − .The distribution of errors in both components of proper motionis given in Fig. 12.The radial velocity is measured by the on-board radial veloc-ity spectrometer. This instrument is only sensitive to stars downto G RVS =
17 magnitude. We assume an upper limit on the er-ror in radial velocity of 20 km · s − , and assume that stars witha precision worse than this will not be given any radial velocityinformation.Of the 523 million measured individual Milky Way stars, 74million have a radial velocity measurement. The mean error inthe radial velocity measurement is 8.0 km · s − . The distributionof radial velocity error is given for each G magnitude in Fig. 13,and in Fig. 14 split by spectral type. The radial velocity error isgiven as a function of G RVS magnitude in Fig. 16
The end-of-mission error in each measurement as a function of G magnitude is given in Fig. 17.Gaia will produce low-resolution spectra, in addition to mea-suring the magnitude of each source in the Gaia bands G , G BP ,
8. Luri et al.: Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator
G magnitude [mag] P a r a ll a x e rr o r [ µ a s ] Fig. 8.
End-of-mission parallax error against G magnitudefor all single stars. The colour scale represents the log ofdensity of objects in a bin size of 80 mmag by 2.5 µ as.White area represents zero stars.
250 500 750 1000 1250 1500 1750
Real parallax [ µ as] P a r a ll a x E rr o r [ µ a s ] Fig. 9.
End-of-mission parallax error against parallax for allsingle stars. The colour scale represents the log of densityof objects in a bin size of 10 by 2.5 µ as. White area repre-sents zero stars. Real right ascension [deg] R i g h t a s ce n s i o n E rr o r [ µ a s ] C o un t Fig. 10.
Right ascension error against real right ascension.The colour scale is linear, with a factor of 10 . Histogramsare computed for both right ascension and right ascensionerror. The colour scale represents log density of objects in abin size of 2 degrees by 7.5 µ as. White area represents zerostars. −
50 0 50
Real declination [deg] D ec li n a t i o n E rr o r [ µ a s ] C o un t Fig. 11.
Declination error against real declination. Thecolour scale is linear, with a factor of 10 . Histograms arecomputed for both declination and declination error. Thecolour scale represents log density of objects in a bin sizeof 1 degrees by 5 µ as. White area represents zero stars. G RP , and G RVS . Whilst GOG is capable of simulating these spec-tra, they have not been included in the present simulations owingto the long computation time and the large storage space require-ment of a catalogue of spectra for one billion sources.Figure 18 shows the distribution in the error of each photo-metric measurement. As can be seen in this figure, the error in G is much lower than for the other instruments, and for all stars it is less than 8 mmag. The mean error in G is 3.0 mmag. Themean error in G BP and G RP is 14.6 mmag and 7.7 mmag, respec-tively. The mean error in G RVS is 13.2 mmag, although it mustbe remembered that the radial velocity spectroscopy instrumentis limited to brighter than G RVS =
9. Luri et al.: Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator
Radial velocity error [km s − ] C o un t All6-78-910-1112-1314-1516-17
Fig. 13.
Histogram of radial velocity error split by G mag-nitude range. The histogram contains 100% of all data thathave radial velocity information. Radial velocity error [km s − ] C o un t AllOBAFGKM
Fig. 14.
Histogram of radial velocity error split by spectraltype. The histogram contains 100% of all data that haveradial velocity information.
G magnitude [mag] µ α E rr o r [ µ a s y r − ] G magnitude [mag] µ δ E rr o r [ µ a s y r − ] Fig. 15.
2D histograms showing error in proper motion against G magnitude. The colour scale represents log density of objects in abin size of 80 mmag by 2 µ as · yr − . Left is proper motion in right ascension, and right is proper motion in declination. White arearepresents zero stars.structure seen in all four maps is derived from the Gaia scanninglaw.It is interesting to point out the ring in the four plots of Fig.19 caused by the disk of the Galaxy. Owing to significant levelsof interstellar dust in the disk of the Galaxy, visible objects aregenerally much redder. This reddening causes objects to lose fluxat the bluer end of the spectrum, making them appear fainter tothe G BP photometer. Therefore the plane of the Galaxy can beseen as an increase in the mean photometric error in the G BP error map.Conversely, the disk of the Galaxy shows as a ring of de-creased mean photometric error in the G RP and G RVS maps,since the sensitivity of their spectra is skewed more towards theredder end of the spectrum. It is important to note, however, that the e ff ect of crowding on photometry is not accounted forin GOG. Gaia will be continuously imaging the sky over its full five-yearmission, and each individual object will be observed 70 timeson average. The scanning law means that the time between re-peated observations varies, and Gaia will be incredibly usefulfor detecting many types of variable stars. GOG produces a totalof 10.8 million single variable objects. This number comes fromthe UM (Robin et al. 2012) and assumes 100% variability de-tection. The exact detection rates and the classification accuracyfor each variability type are still unknown. In fact, the numbersof variable objects in the catalogue is expected to be higher than
10. Luri et al.: Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator
G [mag] G E rr o r [ mm ag ] G [mag] G B PE rr o r [ mm ag ] G [mag] G R PE rr o r [ mm ag ] G [mag] G R V S E rr o r [ mm ag ] Fig. 17.
End-of-mission errors in photometry as a function of G magnitude. The colour scale represents log density of objects ina bin size of 80 mmag by 0.4 mmag. Top left, G magnitude; top right, G BP ; bottom left, G RP ; bottom right, G RVS . White arearepresents zero stars.10.8 million because some variable star types have not yet beenimplemented (see Robin et al. 2012 for a more detailed descrip-tion).The distribution of relative parallax error is given for eachtype of variable star in Fig. 20. The numbers of each type ofvariable produced by GOG are given in Table 6, along with thenumber of each type that falls below each relative parallax errorlimit.In general, the numbers of variables presented in this paperare lower than in Robin et al. (2012) by a factor of two or three.This is expected, because in the present paper we are exclud-ing all variables that are part of binary or multiple systems, andpresenting the number of single variable stars alone.However, the number of emission variables is higher in thepresent paper. This is due to implementation of new types ofemission stars: Oe, Ae, dMe, and WR stars. These are now in-cluded as emission variables but were not simulated in Robinet al. (2012). Additionally, the number of Mira variable stars is higher in the present paper. This is from an implementation errorin the version of the UM used in Robin et al. (2012), which hasbeen fixed in the version used in the present paper.
Cepheids and RR-Lyrae are types of pulsating variable stars.Their regular pulsation and a tight period-luminosity relationmake them excellent standard candles, and therefore of particu-lar interest in studies of galactic structure and the distance scale.Figure 21 shows the histogram of error in parallax specificallyfor Cepheid and RR-Lyrae variable stars, while Fig. 22 showsthe errors in proper motions for Cepheids and RR-Lyrae.
Adding low-resolution spectral photometers on-board Gaia willmake it capable of providing information on several object pa-
11. Luri et al.: Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object GeneratorVariability type Total σ (cid:36) /(cid:36) < σ (cid:36) /(cid:36) < σ (cid:36) /(cid:36) < . σ (cid:36) /(cid:36) < . σ (cid:36) /(cid:36) < . σ (cid:36) /(cid:36) < . ×
88 74 55 27 7.7 1.4Emission 3.3 ×
99 97 92 62 16 2.4Flaring 2.1 ×
99 99 98 88 33 4.6 δ Scuti 3.3 ×
90 78 61 35 13 3.5Semiregular 3.6 ×
92 82 68 40 14 1.4Gammador 6.0 ×
91 80 63 35 13 3.2RR Lyrae AB-type 2.4 ×
67 45 25 7.9 1.0 0.1Mira 2.3 ×
92 83 70 44 16 1.2ZZ Ceti 1.9 ×
100 100 99 94 33 4.1ACV 3.5 ×
91 80 64 39 15 3.8RR Lyrae C-type 5.6 ×
68 45 25 7.8 0.9 0.1 ρ Ap 3.0 ×
92 82 65 38 14 3.8Cepheid 1.8 ×
95 88 78 59 30 0.1
Table 6.
Total number of single stars of each variability type, and the percentage of each that falls below each relative parallax errorlimit: 500%, 100%, 50%, 20%, 5%, and 1%.
Type Total σ (cid:36) /(cid:36) < σ (cid:36) /(cid:36) < . σ (cid:36) /(cid:36) < . ×
58 19 8BIV 1.1 ×
81 42 17BV 2.1 ×
81 38 13AII 6.7 ×
79 42 19AIII 9.5 ×
76 37 16AIV 1.4 ×
80 40 16AV 2.7 ×
81 37 14FII 2.0 ×
81 46 22FIII 1.7 ×
76 33 12FIV 3.6 ×
67 22 7FV 7.9 ×
66 19 5GII 1.6 ×
81 43 20GIII 2.0 ×
61 17 5GIV 3.7 ×
53 11 3GV 1.5 ×
72 23 6KII 2.5 ×
81 43 19KIII 4.0 ×
69 21 7KV 1.1 ×
87 34 9MII 1.1 ×
89 59 32MIII 2.2 ×
85 46 16MV 4.2 ×
99 70 19WD 2 . ×
100 94 42
Table 5.
Total number of single stars for each stellar classifi-cation, along with the percentage that fall below each relativeparallax error limit.rameters including an estimate of line-of-sight extinction, e ff ec-tive temperature, metallicity, and surface gravity. Discussion ofeach individual physical parameter is given below.Provided here are results for an approximation of the resultsof Liu et al. (2012), which reproduces CU8 results statistically Proper motion error [ µ as yr − ] C o un t µ α µ δ Fig. 12.
Error in proper motion for alpha and delta for all singlestars.but not individually for each star. Therefore for detailed analysisof specific object types, care should be taken. Again, due to thevery long tails of the error distributions caused by large numbersof extremely faint stars, the mean values given below should betaken with caution.
Across many fields of astronomy, the e ff ects of extinction on theapparent magnitude and colour of stars can play a major rolein contributing to uncertainty. An accurate estimation of extinc-tion will prove highly useful for many applications of the GaiaCatalogue.Figure 23 shows the comparison between true extinction andthe simulated Gaia estimate. For the vast majority of stars, theGaia estimated extinction lies very close to the true value. Thiscould prove very useful when, for example, using parallax andapparent magnitude data from Gaia because accurate extinctionestimates are required to constrain the absolute magnitude of anobject.
12. Luri et al.: Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator
10 11 12 13 14 15 16 17 G RV S magnitude [mag] R a d i a l V e l o c i t y E rr o r [ k m s − ] Fig. 16.
End-of-mission error in radial velocity against G RVS magnitude. The colour scale represents log density in a bin sizeof 50 mmag by 1 km · s − . White area represents zero stars. Magnitude Error [mmag] C o un t GGBPGRPGRVS
Fig. 18.
Histogram of error in G , G RVS , G RP , and G BP for allsingle stars.Additionally, these results show that the Gaia data will behighly useful in terms of mapping galactic extinction in three di-mensions, thanks to the combination of a large number of accu-rate parallax and extinction measurements. The negative extinc-tion values in Fig. 23 are of course non-physical and are simplythe result of applying a Gaussian random error to stars with nearzero extinction.The discontinuity at A = A < A >
1. This distinc- . . . . . . Relative error in Parallax [ σ $ /$ ] C u m u l a t i v e C o un t SemiRegularCepheidDeltaScutiEmmissionFlairingGammadorMicrolensMiraroApRRabRRcACVZZceti
Fig. 20.
Cumulative histogram of the relative parallax error forall single stars, split by variability type. The histogram rangedisplays 85% of all data.tion was made only for presentation of the results, and the realresults from the DPAC algorithms will not show this discontinu-ity. Liu et al. (2012) report a degeneracy between extinction ande ff ective temperature due to the lack of resolved spectral linessensitive only to e ff ective temperature. For all objects in the GOG catalogue, the measured e ff ectivetemperature ranges between 850 and 102000 K. The error in ef-fective temperature is less than 640 K for all stars, with a meanvalue of 388 K. Figure 23 shows the comparison between trueobject e ff ective temperature and the Gaia estimation. The thinlines visible in Fig. 23 are an artefact from the UM, which usesa Hess diagram to produce stars, leading to some quantisation inthe e ff ective temperature of simulated stars. Metallicity can be estimated by Gaia in the form of [ Fe / H ].Measured values range from -6.5 to + ff erence between real andobserved values, as seen in Fig. 23. The mean error in surface gravity is 0.45 dex. The comparisonbetween real and observed surface gravity can be seen in Fig. 23.As with metallicity, the lines at regular intervals at high gravityin this plot are due to the UM (Robin et al. 2012).
6. Conclusions
The Gaia Object Generator provides the most complete pictureto date of what can be expected from the Gaia astrometric mis-sion. Its simulated catalogue provides useful insight into howvarious types of objects will be observed and how each of theirobservables will appear after including observational errors and
13. Luri et al.: Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator instrument e ff ects. The simulated catalogue includes directly ob-served quantities, such as sky position and parallax, as well asderived quantities, such as interstellar extinction and metallicity.Additionally, the full sky simulation described here is usefulfor gaining an idea of the size and format of the eventual GaiaCatalogue, for preparing tools and hardware for hosting and dis-tribution of the data, and for becomeing familiar with workingwith such a large and rich dataset.In addition to the stellar simulation described in this paper,there are plans to generate other simulated catalogues of interest,such as open clusters, Magallanic Clouds, supernovae, and othertypes of extragalactic objects, so that a more complete versionof the simulated Gaia Catalogue can be compiled.Here we have focussed on the simulated catalogue from theinbuilt Gaia Universe Model, based on the Besanc¸on Galaxymodel. However, GOG can alternatively be supplied with an in-put catalogue generated by the user. This way, simulated datafrom any other model can be processed with GOG to obtainsimulated Gaia observations of specific interest to the individ-ual user. The input can be either synthetic data on a specific staror catalogue, or an entire simulated survey such as those gener-ated using Galaxia (Sharma et al. 2011), provided a minimum ofinput information is supplied (e.g. position, distance, apparentmagnitude, and colour).With GOG, the capabilities of the instrument can be ex-plored, and it is possible to gain insight into the expected per-formance for specific types of objects. While only a subset ofthe available statistics have been reproduced here, it is possibleto obtain the full set of available statistics at request.We are working to make the full simulated catalogue pub-licly available, so that interested individuals can begin workingwith data similar to the forthcoming Gaia Catalogue. Acknowledgements.
GOG is the product of many years of work from a numberof people involved in DPAC and specifically CU2. The authors would like thethank the various CUs for contributing predicted error models for Gaia. The pro-cessing of the GOG data made significant use of the Barcelona SupercomputingCenter (MareNostrum), and the authors would specifically like to thank JaviCasta˜neda, Marcial Clotet, and Aidan Fries for handling our computation anddata handling needs. Additionally, thanks go to Sergi Blanco-Cuaresmo for hishelp with Matplotlib.This work was supported by the Marie Curie Initial Training Networks grantnumber PITN-GA-2010-264895 ITN “Gaia Research for European AstronomyTraining”, and MINECO (Spanish Ministry of Economy) - FEDER throughgrant AYA2009-14648-C02-01, AYA2010-12176-E, AYA2012-39551-C02-01,and CONSOLIDER CSD2007-00050.
References
Babusiaux, C. 2005, in ESA Special Publication, Vol. 576, The Three-Dimensional Universe with Gaia, ed. C. Turon, K. S. O’Flaherty, & M. A. C.Perryman, 417Bailer-Jones, C. A. L. 2011, MNRAS, 411, 435Bailer-Jones, C. A. L., Andrae, R., Arcay, B., et al. 2013, A&A, 559, A74de Bruijne, J. H. J. 2012, Ap&SS, 341, 31Isasi, Y., Figueras, F., Luri, X., & Robin, A. C. 2010, in Highlights of SpanishAstrophysics V, ed. J. M. Diego, L. J. Goicoechea, J. I. Gonz´alez-Serrano, &J. Gorgas, 415Jordi, C., Gebran, M., Carrasco, J. M., et al. 2010, A&A, 523, A48Katz, D., Munari, U., Cropper, M., et al. 2004, MNRAS, 354, 1223Liu, C., Bailer-Jones, C. A. L., Sordo, R., et al. 2012, MNRAS, 426, 2463Masana, E., Isasi, Y., Luri, X., & Peralta, J. 2010, in Highlights of SpanishAstrophysics V, ed. J. M. Diego, L. J. Goicoechea, J. I. Gonz´alez-Serrano,& J. Gorgas, 515Perryman, M. A. C., de Boer, K. S., Gilmore, G., et al. 2001, A&A, 369, 339Perryman, M. A. C. & ESA, eds. 1997, ESA Special Publication, Vol. 1200,The HIPPARCOS and TYCHO catalogues. Astrometric and photometric starcatalogues derived from the ESA HIPPARCOS Space Astrometry MissionRobin, A. C., Luri, X., Reyl´e, C., et al. 2012, A&A, 543, A100Robin, A. C., Reyl´e, C., Derri`ere, S., & Picaud, S. 2003, A&A, 409, 523 Sharma, S., Bland-Hawthorn, J., Johnston, K. V., & Binney, J. 2011, ApJ, 730, 3
14. Luri et al.: Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator
Fig. 19.
HealPixMap in equatorial coordinates of the mean error in:
Top left: G ; top right: G BP ; lower left: G RP ; lower right: G RVS .The colour scale gives the mean photometric error in mmag. The colour scales are di ff erent due to di ff erences in the maximum meanmagnitude. Parallax Error [ µas ] C o un t σ $ Cepheid σ $ RR-Lyrae
Fig. 21.
Histogram of parallax error for Cepheid and RR-Lyrae variable stars. RR-Lyrae is a combination of the twosub-populations RR-ab and RR-c.
Proper Motion Error [ µas ] C o un t σ µ α Cepheid σ µ α RR-Lyrae σ µ δ Cepheid σ µ δ RR-Lyrae
Fig. 22.
Histogram of proper motion error µ α and µ δ forCepheid and RR-Lyrae variable stars. RR-Lyrae is a com-bination of the two sub-populations RR-ab and RR-c.
15. Luri et al.: Overview and stellar statistics of the expected Gaia Catalogue using the Gaia Object Generator − Observed extinction [A ] R e a l e x t i n c t i o n [ A ] log ]2468 C o un t [ l o g ] − − − − Observed metalicity [Fe/H] − − − − R e a l m e t a li c i t y [ F e / H ] log ]2468 C o un t [ l o g ] Observed log gravity [log g ] R e a ll ogg r a v i t y [l og g ] log ]2345678 C o un t [ l o g ] Observed effective temperature [K] R e a l e ff ec t i v e t e m p e r a t u r e [ K ] log ]2468 C o un t [ l o g ] Fig. 23.
Comparison of the true values of physical parameters with the GOG ‘observed’ values for:
Top left , extinction; top right ,metallicity; bottom left , surface gravity; and bottom right , e ff ective temperature. The colour scales represent log density of objectsin a bin size of: top left , 50 by 50 mmag; top right , 0.4 by 0.4 dex; bottom left , 0.5 by 0.5 dex; and bottom right , 100 by 100 K.White area represents zero stars., 100 by 100 K.White area represents zero stars.