Expected Science Performance for the nominal and the extended mission

 

Astrometric Performance             Photometric Performance             Spectroscopic Performance            PyGaia (Python toolkit)

 

Since mid-2014, Gaia has been performing micro-arcsecond (μas) global astrometry for nearly ~2,000 million stars down to G ≈ 20.7 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. Each star transits the astrometric instrument on average ~12 times per year, leading to ~630/1260 CCD detector transits over the nominal/extended (five/ten-year) mission lifetime. Gaia does not exclusively observe stars: all sufficiently point-like objects brighter than G ≈ 20.7 mag are observed, including solar-system objects such as asteroids and Kuiper-belt objects, quasars, supernovae, multiple stars, etc. (while solar-system objects have been published starting with Gaia Data Release 2, results for non-single stars, quasars, and extended objects will be published starting with Gaia Data Release 3). The Gaia CCD detectors feature a pixel size of 10 μm (59 milli-arcsecond) in the scanning direction (also known as the along-scan direction) and the astrometric instrument has been designed to cope with object densities up to some 750,000 stars per square degree. In crowded fields, only the brightest stars are observed such that the completeness limit becomes brighter than 20.7th magnitude in such regions.

Photometric observations are being collected with the photometric instrument, at the same angular resolution as the astrometric observations and for all objects observed astrometrically, in order to:

  • enable chromatic corrections of the astrometric observations;
  • 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.). Astrophysical parameters for selected sources have been part of Gaia Data Release 2 and Gaia Data Release 3 will contain object classifications and astrophysical parameters, together with the spectra they are based on, for spectroscopically and (spectro-)photometrically well-behaved objects;
  • allow reconstruction of photometric time series for photometrically variable objects. Light curves (including epoch photometry) and variable-star classifications of selected sources have been part of Gaia Data Release 2 and Gaia Data Release 3 will contain the same information for a much extended sample. In addition, Gaia Data Release 3 will contain the Gaia Andromeda Photometric Survey (GAPS), consisting of the photometric time series for all sources located in a 5.5°-radius field centred on the Andromeda galaxy.

Spectroscopic observations are being collected with the spectroscopic instrument for all objects down to GRVS ≈ 16 mag, in order to:

  • provide radial velocities through Doppler-shift measurements using cross-correlation (~150 million stars). Median radial velocities for some 7 million bright stars have been published in Gaia Data Release 2 and Gaia Data Release 3 will contain median radial velocities for an extended sample of stars with available atmospheric-parameter estimates;
  • provide (starting with Gaia Data Release 4astrophysical information, such as interstellar reddening, atmospheric parameters, and rotational velocities, for stars brighter than GRVS ≈ 12 mag (~5 million stars); and
  • provide (starting with Gaia Data Release 4) element abundances for stars brighter than GRVS ≈ 11 mag (~2 million stars).

The spectroscopic instrument can cope with object densities up to some 35,000 stars per square degree. In denser areas, only the brightest stars are observed such that the spectroscopic completeness limit becomes brighter than 16th magnitude in such regions.

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 is being 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 ultimately allow to systematically resolve double stars down to separations of ~0.1 arcsec.

In the scientific performance assessments for Gaia presented below, all known instrumental effects have been included under the appropriate in-flight operating conditions (temperature, CCD operating mode, straylight, contamination of the telescopes, etc.). All error sources have been included as random variables with typical (median) deviations (as opposed to best-case or worst-case deviations).

Contrary to pre-launch and post-commissioning astrometric error budgets presented earlier on this website, the current astrometric predictions (published in 2020, based on Gaia EDR3) are based on extrapolations of real data and do no longer contain a 20% scientific contingency margin to cover calibration errors and real-sky complexities. This margin, however, is still contained in the photometric and spectroscopic predictions (which date from 2014 and which are currently under revision).

Two sets of astrometric predictions are presented below:

  • One for the nominal mission, which covers the five-year time interval from mid-2014 to mid-2019. The underlying scientific observations, which have already been collected by the spacecraft and transmitted to ground, are currently being prepared for processing by the Data Processing and Analysis Consortium (DPAC) and will be published as Gaia's fourth data release (Gaia DR4). In practice, it is planned that Gaia DR4 will be based on 5.5 years of science data (rather than 5 years, as assumed here) but this difference will be ignored here and the nominal-mission performance will, for simplicity, be referred to as Gaia DR4.
  • One for the extended mission, which covers the 10-year time interval from mid-2014 to mid-2024. In this case, it has simply been assumed that spacecraft operations and science-data collection will continue until mid-2024, after which DPAC processing will ultimately result in Gaia's fifth data release (Gaia DR5). Needless to say, only time will tell whether the assumed availability of 10 years of science data for Gaia DR5 will be achieved.

The performance numbers presented below refer to the standard errors, i.e., they refer to the precision of the mission data. An assessment of (residual) systematic errors in the Gaia data, linking to its accuracy, is much more difficult to provide. For astrometry, a known contributor to systematic parallax errors are unmodelled spin-synchronous basic-angle variations. The metrology data derived from the basic-angle monitoring device should ultimately allow, after careful calibration, to limit systematic effects to 1 μas in Gaia DR5. Work to achieve this goal is ongoing inside DPAC.

The PyGaia Python toolkit implementing the error models described below is available here.

 

1. Astrometric performance (updated in 2020, based on Gaia EDR3)

The astrometric standard errors for the nominal and for the extended mission (for simplicity denoted "Gaia DR4" and "Gaia DR5", respectively) are extrapolated predictions based on real data, in particular Gaia EDR3 astrometry. As such, the predictions cover all instrumental effects, including the straylight levels as measured in flight, as well as residual calibration errors at ground-processing (DPAC) level. The Gaia EDR3 uncertainties underlying the Gaia DR4 and Gaia DR5 predictions have been inflated by a factor 1.1 to correct for the fact that the external errors of the published astrometry in Gaia EDR3 (like in Gaia DR2) are typically ~10% larger than the formal, published uncertainties. In other words, the earlier 20% science contingency margin to cover (residual) calibration errors and real-sky complexities has been reduced to a 10% inflation to cover remaining model errors in the data processing.

The predicted parallax standard errors σϖ, averaged over the sky for a uniform celestial distribution, are:

    Gaia DR4   Gaia DR5   
Very bright stars (G < 3 mag) See text See text
Bright stars (3 mag < G < 13 mag)   See text See text
G = 13 mag 10 μas 7 μas
G = 14 mag 14 μas 10 μas
G = 15 mag 22 μas 16 μas
G = 16 mag 35 μas 25 μas
G = 17 mag 59 μas 42 μas
G = 18 mag 107 μas 75 μas
G = 19 mag 211 μas 149 μas
G = 20 mag 462 μas 325 μas
G = 20.7 mag 835 μas 588 μas

 

A simple performance model which reproduces the parallax-standard-error estimates listed above, is:

σϖ [μas] = Tfactor · (40 + 800 · z + 30 · z2)1/2,

where

  • Tfactor = 0.749 for Gaia DR4 and 0.527 for Gaia DR5 represents the temporal improvement factor in the parallax uncercainty allowed by adding more data that span a longer time interval; 
  • z = MAX[100.4 · (13 - 15), 100.4 · (G - 15)] is an auxiliary variable representing an inverse G-band photon flux;
  • G - in the range 3-20.7 mag - denotes the broad-band, white-light, Gaia magnitude (see below).

The MAX function in the equation for z above allows to apply the simple performance model also in the bright-star magnitude range 3 ≤ G ≤ 13 mag and returns a constant bright-star parallax noise floor at σϖ = 10 μas and 7 μas for Gaia DR4 and Gaia DR5, respectively. However, despite this formal and seemingly precise prediction, these numbers should be treated with great care. For these stars, nominal yet shorter CCD integration times (through the use of TDI gates) are being used to limit saturation and the actual Gaia DR4 and Gaia DR5 performance depends sensitively on magnitude as well as on the adopted TDI-gate scheme and its associated residual calibration errors, which contribute significantly for bright stars yet which are notoriously difficult to predict forward in time. As a result, Gaia DR4 and Gaia DR5 performance predictions for bright stars are very uncertain.

All so-called very bright stars (G < 3 mag) are being observed with a special (SIF) mode, the data of which is not (yet) treated in the standard data-processing pipelines. Depending on how well this mode can ultimately be calibrated, parallax standard errors at the level of a few dozen μas could potentially be achieved for these objects. This remains the topic of ongoing work.

For sky-averaged position and proper-motion errors, σ0 [μas] and σμ [μas yr-1], the following scaling relations can be used:

    Gaia EDR3     Gaia DR4   Gaia DR5   
σ0 0.75 · σϖ 0.75 · σϖ 0.75 · σϖ
                   σα*                     0.80 · σϖ                     0.80 · σϖ                     0.80 · σϖ
                 σδ                     0.70 · σϖ                     0.70 · σϖ                     0.70 · σϖ
σμ 0.96 · σϖ 0.54 · σϖ 0.27 · σϖ
                   σμα*                     1.03 · σϖ                     0.58 · σϖ                     0.29 · σϖ
                  σμδ                     0.89 · σϖ                     0.50 · σϖ                     0.25 · σϖ

 

where the asterisk denotes true arcs on the sky (σα* = σα · cos(δ), etc.).

 

2. Photometric performance (updated in 2014, supported by Gaia DR2)

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. Photometric relationships between the Gaia broad-band G and other photometric systems can be found here.

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 nominal 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 in flight. These figures show the single-field-of-view-transit photometric standard errors as function of G magnitude and V-IC colour index (see Jordi et al. 2010). 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 and which includes 20% science margin is:

σG [mag] = 1.2∙10-3 ∙ (0.04895 ∙ z2 + 1.8633 ∙ z + 0.0001985)1/2,

where z = MAX[100.4 ∙ (12 - 15), 100.4 ∙ (G - 15)].

For the BP/RP photometers, there is a V-IC colour 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.

The above parametrisations for BP and RP also have 20% science margin included (through the a,b,c coefficients).

Sky-average end-of-nominal-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 for the nominal, five-year mission). With an assumed calibration error of 3 milli-magnitude at CCD level for the G band and 5 milli-magnitude at CCD level for the BP/RP bands, the following end-of-nominal-mission median-straylight photometric errors, in units of milli-magnitude, would be reached (including 20% margin for G, BP, and RP):

  B1V G2V M6V
G [mag] G BP RP G BP RP G BP RP
3 - 13 0.2 1 1 0.2 1 1 0.2 1 1
14 0.2 1 1 0.2 1 1 0.2 2 1
15 0.2 1 2 0.2 1 1 0.2 5 1
16 0.4 2 3 0.4 2 2 0.4 10 1
17 0.6 3 6 0.6 4 4 0.6 25 2
18 0.9 6 15 0.9 9 8 0.9 63 4
19 1.8 15 37 1.8 23 20 1.8 157 8
20 3.7 37 91 3.7 56 48 3.7 395 20

 

These numbers are based on in-flight experience and are supported by Gaia's second data release (Gaia DR2).

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 are not homoscedastic but heteroscedastic. If, for particular investigations such as variability studies, photometric standard errors for other than median straylight levels are needed, click here.
 

3. Spectroscopic performance (updated in 2014, supported by Gaia DR2)

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 (see Cropper et al. 2018). Over the five-year nominal 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 nominal 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-nominal mission composite spectra as function of instrumental magnitude GRVS.

The robust-formal-error calculation includes all known instrumental effects, including straylight as measured in flight. 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.

The predicted end-of-nominal-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]

B1V <7.5 <1
11.3 15
G2V <12.3 <1
15.2 15
  K1III-MP (metal-poor)   <12.8 <1
15.7 15

 

These numbers are based on in-flight experience and are supported by Gaia's second data release (Gaia DR2). They do include 20% science margin.

A simple performance model which reproduces the end-of-mission radial-velocity robust formal error estimates listed above, is:

σvrad [km s-1] = σfloor + 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. The quantity σfloor denotes the bright-star noise floor. Expectations are that the bright-star noise floor will ultimately come down to a level of ~0.5 km s-1, and possibly better. The above 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 Jordi et al. 2010). Systematics in the radial velocities are expected to be kept under control to within a few 100 m s-1.