25 YEARS AFTER THE DISCOVERY: SOME CURRENT TOPICS ON LENSED QSOs

25 YEARS AFTER THE DISCOVERY: SOME CURRENT TOPICS ON LENSED QSOs

Santander (Spain), 15th-17th December 2004

Transverse velocities of QSOs from microlensing parallax

Tyoma Tuntsov, Mark Walker and Geraint Lewis

Sydney Uni

Outline of the talk

• What is the annual parallax effect?

• How can it be used to determine the transverse velocity in the system?

• Where can we find the effect?

• (Bad) Illustration – QSO2237+0305

• Conclusions and Outlook

• What is the annual parallax effect?• Natural formalism for microlensing• What is the annual parallax effect?• What is it telling us?

• How can it be used to determine the transverse velocity in the system?

• Where can we find the effect?

• (Bad) Illustration – QSO2237+0305

• Conclusions and Outlook

Outline of the talk

Natural formalism for microlensing(Gould, 2000, ApJ, 542, 785)

• All quantities projected onto observer plane• Coordinate frame is fixed by source and lens• Many things (those related to observer motion) look simpler!

What is the annual parallax effect?

constF 0

),()(0 ttFF r )()(

),(lg5.20

ttt

tmm

ervr

r

What is it telling us?

),( tr

• Galaxy: Optical depth is low

Schwarzschild lens model for

Er

ty

yy

y

|)(|

4

2)(

0

2

2

rr

r

OGLE-1999-Bulge-19 (Smith et al., 2002, MNRAS, 336, 670)

What is it telling us?

),( tr

• Galaxy: Optical depth is low

Schwarzschild lens model for

• Microlensed QSOs:

can be anything

Er

ty

yy

y

|)(|

4

2)(

0

2

2

rr

r

),( tr1~

What is it telling us?

),( tr

• Galaxy: Optical depth is low

Schwarzschild lens model for

• Microlensed QSOs:

can be anything

Er

ty

yy

y

|)(|

4

2)(

0

2

2

rr

r

),( tr1~

What is it telling us?

),( tr

• Galaxy: Optical depth is low

Schwarzschild lens model for

• Microlensed QSOs:

can be anything

Er

ty

yy

y

|)(|

4

2)(

0

2

2

rr

r

),( tr1~

What is it telling us?

),( tr

• Galaxy: Optical depth is low

Schwarzschild lens model for

• Microlensed QSOs:

can be anything

Use Taylor expansion:

Er

ty

yy

y

|)(|

4

2)(

0

2

2

rr

r

),( tr1~

))(()()( 000 rr tttt

t

What is it telling us?

)()( 0 ttt ervrr

)( 00 ttTmm ii

),( yxe r

),( YXm

mt

mT

v

)()( 00 yyYxxX ii

mtttt

mmtm ))(()()( 000 rr

• What is the annual parallax effect?• How can it be used to determine the

transverse velocity in the system?– Correlation between (T, X, Y)

coefficients in different images– Individual velocities and magnification

matrices

• Where can we find the effect?• (Bad) Illustration – QSO2237+0305• Conclusions and Outlook

Outline of the talk

Correlations between (T, X, Y) coefficients in different images

mt

mT

v

jj mT v

jjj YXT yx vv

Thus, at least three images required

mtttt

mmtm ))(()()( 000 rr

Individual velocities and magnification matrices

jjj uAvv ˆ0

)|ˆ|( 1 jj A

0|ˆ| vuA jj• Assume

OR• Use independent regions of O-plane plus additional info

• What is the annual parallax effect?

• How can it be used to determine the transverse velocity in the system?

• Where can we find the effect?– Order-of-magnitude argument– QSO wish list

• (Bad) Illustration – QSO2237+0305

• Conclusions and Outlook

Outline of the talk

Order-of-magnitude argument

• How good is linear approximation?

• Rescaling to Einstein units:

mmtmm e )(0 rv

mrr

tmm E

E

e

rv

0

22)( Dt erv

mDrr

tE

E

e

2

2

2rv

Order-of-magnitude argument

• How good is linear approximation?

• Rescaling to Einstein units:

mmtmm e )(0 rv

mrr

mrr

tmm E

E

eE

E

rv

0

22)( Dt erv

mDrr

tE

E

e

2

2

2rv

Order-of-magnitude argument

• How good is linear approximation?

• Rescaling to Einstein units:

mmtmm e )(0 rv

mrr

mrr

tmm E

E

eE

E

rv

0

22)( Dt erv

mDrr

tE

E

e

2

2

2rv

Signal S

Order-of-magnitude argument

• How good is linear approximation?

• Rescaling to Einstein units:

mmtmm e )(0 rv

mrr

mrr

tmm E

E

eE

E

rv

0

22)( Dt erv

mDrr

tE

E

e

2

2

2rv

Noise N

Signal S

Order-of-magnitude argument

• ,

•

– Optimal t ~ 1 year

•

1~mrE

mrr

tS E

E

e )(r

mDrr

tN E

E

2

2

2v

1~22DrE

mDr

r

t

r

rNS E

EE

e2

2

2

::v

Go Green

LS

SLLE D

DD

cGMzr 24)1(

Go Green(if it works)

LS

SLLE D

DD

cGMzr 24)1(

LSL

SLcr DD

DGcz 4)1(2

Go Green(if it works)

LS

SLLE D

DD

cGMzr 24)1(

LSL

SLcr DD

DGcz 4)1(2

QSO Wish List

• Redshifts of order unity

QSO Wish List

• Redshifts of order unity• Highly symmetric configuration

• Intrinsic variability constraint• bulk velocity constraints

QSO Wish List

• Redshifts of order unity• Highly symmetric configuration

• Intrinsic variability constraint• bulk velocity constraints

• The lens is NOT:• a virialized cluster member• massive elliptic galaxy

QSO Wish List

• Redshifts of order unity• Highly symmetric configuration

• Intrinsic variability constraint• bulk velocity constraints

• The lens is NOT:• a virialized cluster member• massive elliptic galaxy

• The system is not far from the direction of Solar system motion with respect to CMB (additional 350 km/s)

QSO Wish List

• Redshifts of order unity• Highly symmetric configuration

• Intrinsic variability constraint• bulk velocity constraints

• The lens is NOT:• a virialized cluster member• massive elliptic galaxy

• The system is not far from the direction of Solar system motion with respect to CMB (additional 350 km/s)• Narrow-band observations are possible

QSO Wish List

• Redshifts of order unity• Highly symmetric configuration

• Intrinsic variability constraint• bulk velocity constraints

• The lens is NOT:• a virialized cluster member• massive elliptic galaxy

• The system is not far from the direction of Solar system motion with respect to CMB (additional 350 km/s)• Narrow-band observations are possible

And it should be bright, favourably located on the sky, year-around observable etc..

• What is the annual parallax effect?

• How can it be used to determine the transverse velocity in the system?

• Where can we find the effect?

• (Bad) Illustration – QSO2237+0305

• Conclusions and Outlook

Outline of the talk

Application to QSO2237+0305

OGLE-II (Wozniak et al., 2000, ApJ, 529, 88)

Application to QSO2237+0305

OGLE-II (Wozniak et al., 2000, ApJ, 529, 88)

Weird velocities

• Effective transverse velocity

• Using a different method

(Schmidt, Webster & Lewis, 1998, MNRAS, 295, 488)

km/s)21,715(0 vkm/s)42,205( Av

km/s)64,2024( Bv

km/s)207,11014( Cv

km/s)17,420( Dv

km/s)22,98(0 vkm/s)54,2042( Au

km/s)712,1749( Bu

km/s)201,4020( Cu

km/s)216,513( Du

• What is the annual parallax effect?

• How can it be used to determine the transverse velocity in the system?

• Where can we find the effect?

• (Bad) Illustration – QSO2237+0305

• Conclusions and Outlook

Outline of the talk

Conclusions and Outlook

• Photometric monitoring of some QSOs can help determine 3D picture of their motion

• Little chance to know

a priori where the method will work

• Photometric accuracy is most important

• More data are needed• Try it yourself!

Thank you for your attention!