The Tycho-Gaia Astrometric Solution (TGAS) · The reference frame of Gaia DR1 The ICRS = International Celestial Reference System (IAU 1997) is the basis for all modern astrometric

IAUS 330: Astrometry and Astrophysics in the Gaia sky. 24-28 April 2017, Nice, France

The Tycho-Gaia Astrometric Solution (TGAS)

Lennart LindegrenLund Observatory, Sweden

Outline of talk

• Historical background and concept

• Reference frame of TGAS

• Uncertainties

• Correlations

• Systematics

• Conclusions

2

The Hipparcos instrument

Main detector:• pre-selected stars• one channel (Hp)➜ Hipparcos Catalogue

Auxiliary starmapper detectors for guidance:• no pre-selection• two channels (BT, VT)➜ Tycho/Tycho-2 Catalogue

3

Hipparcos (1989-1993)

5 6 7 8 9 10 11 12 13 14

G [mag]

0:1

0:2

0:5

1

2

5

10

20

50

100

200

500

Standard

uncert

ain

tyofRA

(1991:2

5)

[mas]

Hip subset

Tyc subset

Q90

Q50

Q10

HipparcosTycho-2

Hipparcos and Tycho-2: Positional errors at 1991.25

Tycho-2 Catalogue2.5 million stars(Høg et al. 2000)

Hipparcos Catalogue118,000 stars(van Leeuwen 2007)

4Magnitude

Sta

ndar

d un

certa

inty

in R

.A. [

mas

]

From HTPM to TGAS

• In 2009 François Mignard proposed the Hundred Thousand Proper Motions (HTPM) project as an early “appetizer” for things to come from the Gaia mission

• Basic idea: to get a 10-fold improvement of the Hipparcos proper motions from early Gaia observations of Hipparcos stars, using the >20 yr epoch difference

5

• HTPM was adopted as part of Gaia DR1 in the official data release scenario

• A natural extension of HTPM is to use Tycho-2 positions as well➜ Tycho-Gaia Astrometric Solution (TGAS) (Michalik et al., A&A 574, A115, 2015)

• TGAS allowed us to verify Gaia’s astrometric performance and improve the calibration models about 1 year earlier than otherwise possible

Astrometric model for a single star

Time [yr]0 1 2 3 4 5

Ang

leapparent

stellar path position &

proper motion

parallax (ϖ)Five astrometric parameters per starFive astrometric parameters per starα barycentric right ascension at 2015.0

δ barycentric declination at 2015.0

ϖ parallax

µα* proper motion in R.A. (× cos δ)

µδ proper motion in declination

6

Degeneracy for < 1 yr of observations

early Gaiaobservations

Time [yr]0 1 2 3 4 5

Ang

le

7

??

??

TGAS: Using the old position as prior

Hipparcosor Tycho-2

position(1991.25)

early Gaiaobservations

8

➜ Two distinct subsets in TGAS:• Hip subset (~90,000 stars) using Hipparcos positions• Tyc subset (~2 million stars) using Tycho-2 positions

Only positions were taken from Hipparcos and Tycho-2, no parallaxes or proper motions!

Starting with Gaia DR2, no prior information from Hipparcos and Tycho-2 will be used

The reference frame of Gaia DR1

The ICRS = International Celestial Reference System (IAU 1997) is the basis for all modern astrometric catalogues (replacing FK4, FK5, equinox B1950, J2000, etc)

ICRS is non-rotating with respect to distant quasars − orientation defined by radio (VLBI) observations of ~300 quasars

Before Gaia, the Hipparcos Catalogue was the best optical realisation of the ICRS

9

ն�,,&56ܟ = ն�,+,3ܟ � �.�� sin չ cos ն+ �.�� sin չ sin ն� �.�� cos չչ,,&56ܟ = չ,+,3ܟ + �.�� sin ն+ �.�� cos ն

Both Hipparcos and TGAS are nominally on ICRS

But we find that the Hipparcos Reference Frame rotates wrt ICRS by 0.24 mas/yr :

Five astrometric parameters per star:

Five standard uncertainties:ֆն�, ֆչ, ֆ, ֆܟն�, ֆܟչ

ն, չ, , ,�նܟ չܟ

Uncertainties in TGAS

ra, dec, parallax, pmra, pmdec

ra_error, dec_error, ...

Gaia Archive:

10

5 6 7 8 9 10 11 12 13 14G [mag]

0:01

0:02

0:05

0:1

0:2

0:5

1

2

5

10Sta

ndar

dunce

rtai

nty

ofPM

inRA

[mas

yr¡

1]

11

Tyc subset(astrometric_priors_used = 5)

Hip subset(astrometric_priors_used = 3)

Standard uncertainty in proper motion versus magnitude

G magnitude

Sta

ndar

d un

certa

inty

of P

M in

R.A

. [m

as/y

r]

Standard uncertainty in parallax versus magnitude

5 6 7 8 9 10 11 12 13 14G [mag]

0

0:1

0:2

0:3

0:4

0:5

0:6

0:7

0:8

0:9

1:0

1:1

Sta

ndar

dunce

rtai

nty

ofpar

alla

x[m

as]

Hip subset Tyc subset

12G magnitude

Sta

ndar

d un

certa

inty

in p

aral

lax

[mas

]5 6 7 8 9 10 11 12 13 14

G [mag]

0

0:1

0:2

0:3

0:4

0:5

0:6

0:7

0:8

0:9

1:0

1:1

Sta

ndar

dunce

rtai

nty

ofpar

alla

x[m

as]

Sta

ndar

d un

certa

inty

in p

aral

lax

[mas

]

G magnitude

Median standard uncertainty in parallax versus position

0

0:1

0:2

0:3

0:4

0:5

0:6

0:7

0:8

0:9

1:0

Med

ian

par

alla

xunce

rtai

nty

[mas

]

0

0:1

0:2

0:3

0:4

0:5

0:6

0:7

0:8

0:9

1:0

Med

ian

par

alla

xunce

rtai

nty

[mas

]


13

Five astrometric parameters per star:

Five standard uncertainties:

Ten correlation coefficients (−1 < ρ < 1):

ֆն�, ֆչ, ֆ, ֆܟն�, ֆܟչ

ն, չ, , ,�նܟ չܟ

ք(ն, չ), ք(ն,), ք(ն,ܟն�), ք(ն,ܟչ),ք(չ,), ք(չ,ܟն�), ք(չ,ܟչ),

ք(ܟ,ն�), ք(ܟ,չ),ք(ܟն�,ܟչ)

Correlations in TGAS

ra, dec, parallax, pmra, pmdec

ra_error, dec_error, ...

ra_dec_corr, ...

Gaia Archive:

14

• Correlation coefficients (ρ) are needed for error propagation involving more than one astrometric parameter, e.g.:

Y7 = /ܟ��.��ֆY7Y7

��=

�ֆܟܟ

��+

�ֆ

�� ք(ܟ,)

�ֆܟܟ

� �ֆ

�

⎫⎪⎬⎪⎭neglecting this cangive very wrong σvT

Correlations matter!

⇒

15

• Also when estimating model parameters (chi-square fitting, MLE, Bayesian analysis, ...):

(C = covariance matrix)֊� =�ӹܟն� ӹܟչ ӹ

�&&&��

�

�ӹܟն�ӹܟչӹ

�

�

¡1:0

¡0:8

¡0:6

¡0:4

¡0:2

0

0:2

0:4

0:6

0:8

1:0

Cor

rela

tion

coe±

cien

t

Median correlation coefficient (ϖ, µα*) versus position

¡1:0

¡0:8

¡0:6

¡0:4

¡0:2

0

0:2

0:4

0:6

0:8

1:0

Cor

rela

tion

coe±

cien

t


16

Median correlation coefficient (ϖ, µδ) versus position

¡1:0

¡0:8

¡0:6

¡0:4

¡0:2

0

0:2

0:4

0:6

0:8

1:0

Cor

rela

tion

coe±

cien

t

¡1:0

¡0:8

¡0:6

¡0:4

¡0:2

0

0:2

0:4

0:6

0:8

1:0

Cor

rela

tion

coe±

cien

t


17

Median correlation coefficient (µα*, µδ) versus position

¡1:0

¡0:8

¡0:6

¡0:4

¡0:2

0

0:2

0:4

0:6

0:8

1:0

Cor

rela

tion

coe±

cien

t

¡1:0

¡0:8

¡0:6

¡0:4

¡0:2

0

0:2

0:4

0:6

0:8

1:0

Cor

rela

tion

coe±

cien

t


18Correlations often approach ±1 in the Tycho subset!

Correlations depend on the strength of the prior

19

0:1 0:2 0:5 1 2 5 10 20 50 100 200 500

Prior (1991:25) uncertainty in R:A: [mas]

¡1:0

¡0:8

¡0:6

¡0:4

¡0:2

0

0:2

0:4

0:6

0:8

1:0

Corr

ela

tio

ncoe±

cie

nt

para

llax

pm

racorr

Hip subset

Tyc subset

Cor

rela

tion

coef

ficie

nt p

aral

lax

/ pm

ra

Prior (1991.25) uncertainty in R.A. [mas]

weak prior

strong prior

Systematic errors in TGAS

• Systematic errors exist, and are complicated (largely unknown) functions of position, magnitude, colour, prior used, ...

• Systematics have been investigated through– comparison with external data (e.g. Hipparcos)

20

¡0:5 0 0:5 1:0 1:5 2:0 2:5 3:0

Colour index V¡ I [mag]

¡3

¡2

¡1

0

1

2

3Para

llax

di®

ere

nce

(T¡

H)

[mas]

Example: ϖTGAS − ϖHIP versus colour index

β > 0 (ecliptic north)

β < 0 (ecliptic south)

➜ Colour & position dependent systematicson the level ±0.1 mas

21

Median difference for:


• Systematic errors exist, and are complicated (largely unknown) functions of the position, magnitude, colour, prior used, ...

• Systematics have been investigated through– comparison with external data (e.g. Hipparcos)– special validation solutions (e.g. splitting the data and making separate solutions)

22

Example: Splitting the observations in two datasets

SM1

SM2

AF1

AF2

AF3

AF4

AF5

AF6

AF7

AF8

AF9

BP

RP

RVS1

RVS2

RVS3

WFS2

WFS1

BAM2

BAM1

“early” “late”

Gaia astrometricfocal plane

23

Parallax difference between two validation solutions for “early” and “late” data

“Late” minus “early” data

24


• Systematic errors exist, and are complicated (largely unknown) functions of the position, magnitude, colour, prior used, ...

• Systematics have been investigated through– comparison with external data (e.g. Hipparcos)– special validation solutions (e.g. splitting the data and making separate solutions)

• For the parallaxes– a global offset of ±0.1 mas may be present– there are colour dependent, spatially correlated errors of ±0.3 mas– in small areas even reaching ±1 mas

• These systematics are included in the standard uncertainties– see Gaia DR1 papers (A&A 595, 2016) for details

25

Conclusions

• The reference frame of Gaia DR1 is not the same as the Hipparcos Reference Frame(although both are nominally on ICRS)

• TGAS consists of two subsets: astrometric_priors_used = 3 (Hip) or 5 (Tyc),with very different properties − decisive factor is the strength of the prior

• Correlations in TGAS are very important, especially for weak priors (faint Tyc subset)

• Systematics are at the few 0.1 mas or mas/yr level, probably higher for weak priors

• Future Gaia data releases will tell us how good or bad TGAS really is!

26

Documents

The Tycho-Gaia Astrometric Solution (TGAS) · The reference frame of Gaia DR1 The ICRS = International Celestial Reference System (IAU 1997) is the basis for all modern astrometric