25 years after the discovery: some current topics on lensed qsos
DESCRIPTION
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? - PowerPoint PPT PresentationTRANSCRIPT
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!