Gaia will perform micro-arcsecond (μas) global astrometry for all ~1,000 million stars down to G ≈ 20 mag — except for the ~6,000 brightest stars in the sky — by linking objects with both small and large angular separations in a network in which each object is connected to a large number of other objects in every direction. Over the five-year mission lifetime, a star transits the astrometric instrument on average ~70 times, leading to ~630 CCD transits. Gaia will not exclusively observe stars: all objects brighter than G ≈ 20 mag will be observed, including solar-system objects such as asteroids and Kuiper-belt objects, quasars, supernovae, multiple stars, etc. The Gaia CCD detectors feature a pixel size of 10 μm (59 milli-arcsecond) and the astrometric instrument has been designed to cope with object densities up to 750,000 stars per square degree. In denser areas, only the brightest stars are observed and the completeness limit will be brighter than 20th magnitude.
Photometric observations will be collected with the photometric instrument, at the same angular resolution as the astrometric observations and for all objects observed astrometrically, to:
- enable chromatic corrections of the astrometric observations, and
- provide astrophysical information for all objects, including astrophysical classification (for instance object type such as star, quasar, etc.) and astrophyscial characterisation (for instance interstellar reddenings and effective temperatures for stars, photometric redshifts for quasars, etc.).
Spectroscopic observations will be collected with the spectroscopic instrument for all objects down to GRVS ≈ 16 mag, to:
- provide radial velocities through Doppler-shift measurements using cross-correlation (~150 million stars);
- provide astrophysical information, such as interstellar reddening, atmospheric parameters, and rotational velocities, for stars brighter than GRVS ≈ 12 mag (~5 million stars); and
- provide element abundances for stars brighter than GRVS ≈ 11 mag (~2 million stars).
The spectroscopic instrument has been designed to cope with object densities up to 36,000 stars per square degree. In denser areas, only the brightest stars are observed and the completeness limit will be brighter than 16th magnitude.
In the scientific performance assessments for Gaia, all known instrumental effects are included under the appropriate in-flight operating conditions (temperature, CCD operating mode, etc.). All error sources are included as random variables with typical deviations (as opposed to best-case or worst-case deviations). All performance estimates include a 20% contingency margin. This margin is a DPAC science margin, neither meant for nor available to the Gaia industrial prime contractor. The science margin is assumed to cover, among others:
- "scientific uncertainties" in the on-ground data analysis, including uncertainties related to relativistic corrections, aberration corrections, and the spacecraft and solar system ephemeris;
- scientific effects such as the contribution to the astrometric error budget from the mismatch between the actual and the calibrating point spread function, estimation errors in the sky background and total detection noise values that need to be fed to the centroiding algorithm, etc.;
- the fact that the sky does not contain, as assumed for the performance assessments, "perfect stars" but "normal stars", which can be photometrically variable, have spectral peculiarities such as emission lines, have unrecognised companions, be located in crowded fields, etc.;
- other astronomical environmental factors such as, e.g., localised enhanced sky-background surface brightness, unrecognised small-scale sky-background-brightness gradients, unrecognised prompt particle events, etc.
The PyGaia Python toolkit implementing the error models described below is available here.
1. Astrometric performance
The astrometric standard errors are calculated following the recipe outlined in GAIA-JDB-022. The standard-error calculation includes all known instrumental effects. For instrument-related residual calibration errors at ground-processing (DPAC) level, an appropriate calibration error is included. So-called residual "scientific calibration errors" (e.g., mismatch of the model point spread function, sky-background estimation errors, etc.), all of which result from the on-ground data processing, are not included. These latter errors are assumed to be covered by the 20% science margin.
At the time of the Gaia Mission Critical Design Review (April 2011), the predicted end-of-mission parallax standard errors σπ, averaged over the sky for a uniform distribution, for unreddened B1V, G2V, and M6V stars are:
| || B1V || G2V || M6V |
|Bright stars || 5-14 μas (6 mag < V < 12 mag) || 5-14 μas (6 mag < V < 12 mag) || 5-14 μas (8 mag < V < 14 mag) |
|V = 15 mag||26 μas||24 μas||9 μas|
|V = 20 mag||330 μas||290 μas||100 μas|
A simple performance model, including a V-IC colour term representing the widening of the point spread function at longer wavelengths, which reproduces the end-of-mission parallax-standard-error estimates listed above, is:σπ [μas] = (9.3 + 658.1 · z + 4.568 · z2)1/2 · [0.986 + (1 - 0.986) · (V-IC)],
wherez = MAX[100.4 · (12 - 15), 100.4 · (G - 15)],
and G - in the range 6-20 mag - denotes the broad-band, white-light, Gaia magnitude (see below). Due to their extreme brightness, Gaia will not be able to observe the ~6,000 brightest stars in the sky, those with G < 6 mag; this figure provides the limiting V magnitude as function of V-IC colour index. For stars fainter than G = 6 mag yet brighter than G = 12 mag, data will be acquired: shorter CCD integration times (through the use of TDI gates) will be used to avoid saturation. For these stars, the end-of-mission performance depends sensitively on the adopted TDI-gate scheme, which is not yet frozen and configurable in flight, as well as on magnitude. This is reflected in the quoted performance range 5-14 μas. The MAX function in the equation for z above allows to ignore the TDI-gate "complication" and returns a constant bright-star parallax noise floor, at σπ = 7 μas, for stars with 6 ≤ G ≤ 12 mag. This table and figure provide the sky-averaged end-of-mission parallax standard error as function of G magnitude as predicted by the model. The astrometric precision per single focal-plane crossing is roughly 4.3 times worse than the end-of-mission astrometric precision. Beware that the interpretation of single-crossing precisions is non-trivial: e.g., one transit does not provide a parallax measurement and, moreover, allows only a one-dimensional measurement.
For sky-averaged position and proper-motion errors, σ0 [μas] and σμ [μas yr-1], the following relations can be used, derived from scanning-law simulations:
|σ0||=||0.743 · σπ;|
|σα*||=||0.787 · σπ;|
|σδ||=||0.699 · σπ;|
|σμ||=||0.526 · σπ;|
|σμα*||=||0.556 · σπ;|
|σμδ||=||0.496 · σπ,|
where the asterisk denotes true arcs on the sky (σα* = σα · cos(δ), etc.). End-of-mission standard-error sky maps of various astrometric parameters are accessible here.
The predicted standard errors vary over the sky as a result of the scanning law. The mean (ecliptic-longitude-averaged) variations with ecliptic latitude β are shown in this figure and given in this table, derived from scanning-law simulations. The (approximate) ecliptic latitude can be calculated from the equatorial coordinates (α, δ) or the galactic coordinates (l, b) using:
|sin(β)||=||0.9175 · sin(δ) - 0.3978 · cos(δ) · sin(α)|
| ||=||0.4971 · sin(b) + 0.8677 · cos(b) · sin(l - 6°.38).|
The above recipe provides a simple performance formulation, in combination with the Sloan/Cousins/Johnson magnitude/colour transformations presented in 2010A&A...523A..48J, which gives a prescription for the G magnitude as a function of V and V-IC valid over a wide colour interval. For completeness and for ease of reference, we repeat from 2010A&A...523A..48J the relation to convert Johnson V and Johnson-Cousins V-IC to Gaia G:G = V - 0.0257 - 0.0924 · (V-IC) - 0.1623 · (V-IC)2 + 0.0090 · (V-IC)3,
where the fit error is 0.05 mag. For relations using V-RC, RC-IC, or B-V or for relations linking Sloan magnitudes (g or r) and colours (g-r, g-i, or r-i) to Gaia G magnitudes, see 2010A&A...523A..48J.
2. Photometric performance
Gaia's photometry comprises:
- broad-band white-light G-band fluxes obtained in the astrometric instrument, and
- low-resolution spectro-photometry obtained in the Blue and Red Photometers (BP and RP).
The wavelength coverage of the astrometric instrument, defining the white-light G band, is ~330-1050 nm. The spectral dispersion of the photometric instrument is a function of wavelength and varies in BP from ~3 to ~27 nm pixel-1 covering the wavelength range ~330-680 nm. In RP, the wavelength range is ~640-1050 nm with a spectral dispersion of ~7 to ~15 nm pixel-1. The 76%-energy width of the line-spread function along the dispersion direction varies along the BP spectrum from 1.3 pixels at 330 nm to 1.9 pixels at 680 nm and along the RP spectrum from 3.5 pixels at 640 nm to 4.1 pixels at 1050 nm. Whereas the G-band data are particularly useful for stellar variability studies, the BP/RP spectra allow the derivation of astrophysical parameters, such as interstellar extinctions, surface gravities, etc., needed for the scientific exploitation of the astrometric data. Over the five-year mission lifetime, a star transits the photometric instrument on average ~70 times, leading to ~70 transits in BP and ~70 transits in RP (the dependence on ecliptic latitude is summarised in this table).
The photometric standard errors of the integrated G-band, BP-band, and RP-band are calculated following the recipe outlined in GAIA-JDB-022. The standard-error calculation includes all known instrumental effects as well as a 20% science margin. These figures show the single-field-of-view-transit photometric standard errors, averaged over the sky for a uniform distribution, as function of G magnitude and V-IC colour index (see 2010A&A...523A..48J). As for astrometry, the bright-star errors - which depend sensitively on the adopted TDI-gate scheme, which is not yet frozen and configurable in flight, as well as on magnitude - have been set to a constant noise floor. A simple performance model in the range G = 6-20 mag which reproduces the single-field-of-view-transit photometric standard errors displayed in these figures is:σG [mag] = 10-3 ∙ (0.02076 ∙ z2 + 2.7224 ∙ z + 0.004352)1/2,
where z = MAX[100.4 ∙ (12 - 15), 100.4 ∙ (G - 15)];
σBP/RP [mag] = 10-3 ∙ (10aBP/RP ∙ z2 + 10bBP/RP ∙ z + 10cBP/RP)1/2,
|aBP||=||-0.003201 · (V-IC)3 + 0.0589 · (V-IC)2 + 0.3353 · (V-IC) + 0.7927; |
|bBP||=||-0.001019 · (V-IC)3 + 0.0244 · (V-IC)2 + 0.1756 · (V-IC) + 1.4684;|
|cBP||=||-0.004093 · (V-IC)3 + 0.0740 · (V-IC)2 + 0.2834 · (V-IC) - 3.4772;|
|aRP||=||-0.006560 · (V-IC)3 + 0.1080 · (V-IC)2 - 0.6296 · (V-IC) + 1.4470;|
|bRP||=||-0.003280 · (V-IC)3 + 0.0540 · (V-IC)2 - 0.3148 · (V-IC) + 1.7856;|
|cRP||=||-0.007992 · (V-IC)3 + 0.1482 · (V-IC)2 - 0.7544 · (V-IC) - 3.7232;|
|z||=||MAX[100.4 · (11 - 15), 100.4 · (G - 15)].|
Assuming calibration errors are negligibly small, end-of-mission photometric errors can be estimated by division of the single-field-of-view-transit photometric standard errors by the square root of the number of observations (~70 in average). With an assumed calibration error of 30 milli-mag at CCD-level, the following end-of-mission photometric errors, in units of milli-magnitude, would be reached:
|6 - 13||1||4||4||1||4||4||1||4||4|
|20|| 3 || 29 || 83 || 3 || 43 || 43 || 3 || 301 || 17 |
The Gaia photometric data, sometimes in combination with the astrometric and the spectroscopic data, allow to retrieve astrophysical parameters of objects and to classify them. The accuracy of the estimation of the astrophysical parameters depends on G magnitude and on the value of the parameters themselves. The investigations reported in 2012arXiv1207.6005L, based on simulated BP and RP data, indicate that, for stars at G = 15 mag with less than two magnitudes extinction, effective temperature Teff can be estimated to within 1%, surface gravity log(g) to 0.1-0.2 dex, and metallicity [Fe/H] (for FGKM stars) to 0.1-0.2 dex. Performance degrades at larger extinctions, but not always by a large amount. Extinction can be estimated to an accuracy of 0.05-0.2 mag for stars across the full parameter range with a priori unknown extinction between 0 and 10 mag. Performance degrades at fainter magnitudes, but even at G = 19 mag, log(g) can be estimated to better than 0.2 dex for all spectral types, and [Fe/H] to within 0.35 dex for FGKM stars, for extinctions below 1 mag. The strong and ubiquitous degeneracy in effective temperature and extinction (e.g., 2011MNRAS.411..435B) will limit the accuracy with which either parameter can be estimated at the faintest magnitudes.
3. Spectroscopic performance
Gaia's spectroscopic instrument, the Radial-Velocity Spectrometer (RVS), is an integral-field spectrograph with resolving power ~11,500 covering the wavelength range 847-874 nm. Over the five-year mission lifetime, a star transits the spectroscopic instrument on average ~40 times, leading to ~120 CCD transits.
Radial-velocity robust formal errors are calculated following the recipe outlined in GAIA-JDB-022. The calculation methodology prescribes, for all stars and magnitudes, that a single end-of-mission composite spectrum is first reconstructed by co-addition of all spectra collected during all CCD crossings throughout the five-year mission lifetime. A single mission-averaged radial velocity is then extracted from this end-of-mission composite spectrum by cross correlation with a template spectrum. The spectroscopic performance numbers reported below refer to this prescribed procedure, although it is foreseen in the a posteriori on-ground data analysis by DPAC to actually derive also single-field-of-view transit spectra, and to extract associated epoch radial velocities, whenever this proves possible in practice. As illustration, this figure shows the signal-to-noise ratio of the continuum level of the single-CCD spectra as function of instrumental magnitude GRVS.
The robust-formal-error calculation includes all known instrumental effects. For instrument-related residual calibration errors at ground-processing (DPAC) level, an appropriate calibration error is included. So-called residual "scientific calibration errors" (e.g., template-mismatch errors, residual errors in the derivation of the locations of the centroids of the reference spectral lines used for the wavelength calibration, etc.), all of which result from the on-ground data processing, are not included. These latter errors are assumed to be covered by the 20% science margin.
At the time of the Gaia Mission Critical Design Review (April 2011), the predicted end-of-mission radial-velocity robust formal errors σvrad, averaged over the sky for a uniform distribution, for unreddened B1V, G2V, and K1III-MP (MP = metal-poor) stars are:
| Spectral type || V [mag] || Radial-velocity error [km s-1] |
| K1III-MP (metal-poor) ||13.5||1|
A simple performance model which reproduces the end-of-mission radial-velocity robust formal error estimates listed above, is:σvrad [km s-1] = 1 + b · ea · (V - 14),
where a and b are constants, defined in this table for various spectral types, and V denotes Johnson V magnitude. This performance model, illustrated in this figure, is valid for GRVS ≤ 16.1 mag, with V - GRVS = 0.0119 + 1.2092 · (V-IC) - 0.0188 · (V-IC)2 - 0.0005 · (V-IC)3, where the fit error is 0.07 mag (see 2010A&A...523A..48J). This figure provides the limiting V magnitude as function of V-IC colour index.
The end-of-mission rotational-velocity errors for two rotating B stars and three later-type stars are displayed in this figure, based on GAIA-C6-TN-OPM-PS-006 (restricted access). The expected errors in effective temperature, surface gravity, and metallicity as function of the signal-to-noise ratio of the low-resolution RVS data for thin-disc dwarfs, thick-disc dwarfs, and halo giants is displayed in these figures, taken from 2011A&A...535A.106K. For high-resolution RVS data (stars brighter than 10 mag), the errors are reduced by a factor 2-4, depending on the astrophysical parameter.