|Astrometric Performance Photometric Performance Spectroscopic Performance PyGaia (Python toolkit)|
Gaia will perform micro-arcsecond (μas) global astrometry for all ~1,000 million stars down to G ≈ 20 mag 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) in the scanning direction 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 astrophysical 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 presented below, all known instrumental effects are included under the appropriate in-flight operating conditions (temperature, CCD operating mode, straylight, etc.). The only exception is the slow, continuous contamination of the telescopes which has been discovered during the commissioning phase: the impact of this effect is not included in the current assessment. It is, however, expected that a small number of de-contamination campaigns conducted over the five-year mission will be sufficient to maintain the contamination rates at acceptable levels (i.e., less than 10% transmission loss over the year-year mission, which is comparable to the expected evolution of the light-collection efficiency resulting from radiation damage). 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% scientific contingency margin 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.
Regarding multiple stars, the minimum separation to resolve a close, equal-brightness double star in the on-board star-mapper detector is 0.23 arcsec in the along-scan and 0.70 arcsec in the across-scan direction, independent of the brightness of the primary. During the course of the mission, a given object will be observed many times with 'random' scanning angles meaning that, typically, close double stars may be resolved on board in some transits and stay unresolved in others. In the on-ground processing, however, the full resolution of the astrometric instrument will allow to systematically resolve double stars down to separations of ~0.1 arcsec.
The performance numbers presented below refer to the standard errors, i.e., they refer to the precision of the mission data. An assessment of potential (residual) systematic errors in the Gaia data, linking to its accuracy, is much more difficult to provide. For astrometry, a potential contributor to systematic parallax errors are unmodelled spin-synchronous basic-angle variations. The metrology data derived from the basic-angle monitoring device should allow, after careful calibration, to limit possible systematic effects to 1 μas. Work to achieve this goal is ongoing inside the Data Processing and Analysis Consortium (DPAC).
The PyGaia Python toolkit implementing the error models described below is available here.
The astrometric standard errors are calculated following the recipe outlined in GAIA-JDB-022. The standard-error calculation includes all known instrumental effects, including the straylight levels as measured during the commissioning phase. 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 In-Orbit Commissioning Review (July 2014), 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:
|Bright stars||5-16 μas (3 mag < V < 12 mag)||5-16 μas (3 mag < V < 12 mag)||5-16 μas (5 mag < V < 14 mag)|
|V = 15 mag||26 μas||24 μas||9 μas|
|V = 20 mag||600 μas||540 μas||130 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] = (-1.631 + 680.766 · z + 32.732 · z2)1/2 · [0.986 + (1 - 0.986) · (V-IC)],
z = MAX[100.4 · (12.09 - 15), 100.4 · (G - 15)],
and G - in the range 3-20 mag - denotes the broad-band, white-light, Gaia magnitude (see below). All stars brighter than G = 3 mag will be observed with a special mode. Depending on how well this mode can be calibrated, end-of-mission parallax standard errors at the level of a few dozen μas could potentially be achieved for these stars. This remains the topic of further work. For stars fainter than G = 3 mag yet brighter than G = 12 mag, nominal yet 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 as well as on magnitude. This is reflected in the quoted performance range 5-16 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 3 ≤ 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).|
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 Sloan/Cousins/Johnson magnitude/colour transformations presented in 2010A&A...523A..48J allow estimation of the broad-band Gaia G magnitude as a function of V and V-IC valid over a wide colour interval. 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, please see 2010A&A...523A..48J.
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, including straylight as measured during the in-orbit commissioning phase (July 2014). These figures show the single-field-of-view-transit photometric standard errors as function of G magnitude and V-IC colour index (see 2010A&A...523A..48J). The figures refer to median straylight conditions over a spacecraft rotation period and have 20% margin for the BP and RP bands included. As for astrometry, the bright-star errors - which depend sensitively on the TDI-gate scheme as well as on magnitude - have been set to a constant noise floor. A simple performance model which reproduces the single-field-of-view-transit G-band photometric standard errors displayed in these median-straylight figures is:
σG [mag] = 10-3 ∙ (0.04895 ∙ z2 + 1.8633 ∙ z + 0.0001985)1/2,
where z = MAX[100.4 ∙ (12 - 15), 100.4 ∙ (G - 15)]. This parametrisation for the G band does not carry margin.
For the BP/RP photometers, there is a V-IC dependence, as follows:
σBP/RP [mag] = 10-3 ∙ (10aBP/RP ∙ z2 + 10bBP/RP ∙ z + 10cBP/RP)1/2,
where z = MAX[100.4 ∙ (11 - 15), 100.4 ∙ (G - 15)], and
|aBP||=||-0.000562 · (V-IC)3 + 0.044390 · (V-IC)2 + 0.355123 · (V-IC) + 1.043270;|
|bBP||=||-0.000400 · (V-IC)3 + 0.018878 · (V-IC)2 + 0.195768 · (V-IC) + 1.465592;|
|cBP||=||+0.000262 · (V-IC)3 + 0.060769 · (V-IC)2 - 0.205807 · (V-IC) - 1.866968;|
|aRP||=||-0.007597 · (V-IC)3 + 0.114126 · (V-IC)2 - 0.636628 · (V-IC) + 1.615927;|
|bRP||=||-0.003803 · (V-IC)3 + 0.057112 · (V-IC)2 - 0.318499 · (V-IC) + 1.783906;|
|cRP||=||-0.001923 · (V-IC)3 + 0.027352 · (V-IC)2 - 0.091569 · (V-IC) - 3.042268.|
These parametrisations for BP and RP do have 20% margin included.
Sky-average end-of-mission median-straylight 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 on average). With an assumed calibration error of 30 milli-magnitude at CCD level, the following end-of-mission median-straylight photometric errors, in units of milli-magnitude, would be reached (including 20% margin for G, BP, and RP):
|3 - 13||1.4||4||4||1.4||4||4||1.4||4||4|
Due to the time-variable straylight levels that Gaia experiences over a spin period and hence over the mission, the photometric standard errors of a given source will not be homoscedastic but heteroscedastic. If, for particular investigations such as variability studies, photometric standard errors for other than median straylight levels are needed, click here.
The Gaia spectro-photometric data from the blue and red photometers (BP and RP), sometimes in combination with the astrometric and the RVS spectroscopic data, allow to classify objects and to estimate their astrophysical parameters. A detailed overview of these efforts is given in 2013A&A...559A..74B. The accuracy of the estimation of the astrophysical parameters depends on the G magnitude and on the value of the stellar parameters themselves. Early investigations have been reported in 2012MNRAS.426.2463L. The most recent investigations show that, for FGKM stars at G = 15 mag with less than two magnitudes extinction, effective temperature T_eff can be estimated to within 1-2% (~75 K), surface gravity log(g) to 0.2 dex, and metallicity [Fe/H] to 0.1 dex, using just the BP/RP spectro-photometry. Performance degrades at larger extinctions, but not always by a large amount. Extinction can be estimated to an accuracy of 0.06 mag for all stars at G = 15 mag across the full parameter range with a priori unknown extinction between 0 and 10 mag. The above-quoted performances are somewhat optimistic for two reasons: (1) they are based on pre-launch, no-straylight simulations, and (2) they refer to internal errors, i.e., they assume no significant mismatch between synthetic and real spectra and careful calibration. Without any such calibration, an estimate of the external errors for FGKM stars at G = 15 mag is about 250 K for T_eff, 0.15 mag for extinction, 0.5 dex for log(g), and 0.3 dex for [Fe/H]. Furthermore, 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.
Gaia's spectroscopic instrument, the Radial-Velocity Spectrometer (RVS), is an integral-field spectrograph with resolving power ~11,500 covering the wavelength range 845-872 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 end-of-mission composite spectra as function of instrumental magnitude GRVS.
The robust-formal-error calculation includes all known instrumental effects, including straylight as measured during the in-orbit commissioning phase. 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 In-Orbit Commissioning Review (July 2014), 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]
The bright-star performance is limited by an assumed systematic 1 km s-1 radial-velocity error up to the spectral-type-dependent magnitude limit shown in the table above.
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 - 12.7),
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 up to ~16 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).