Can We Measure H0 with VLBI Observations of Gravitational Images?

We have used the relative positions and magnifications of the A and B images in the gravitational lens system 0957+561, obtained from VLBI observations, to constrain a model for the surface mass distribution of the lens. With measurements of the difference ΔτBA in propagation times associated with A and B (the “relative time delay”) and of the velocity dispersion of the main lensing galaxy, both to be obtained, our model will yield a value for H0 with an uncertainty of ∼ 20% due mainly to uncertainties in our assumptions.

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Multi-frequency VLBI Observations of the Gravitational Lens B0218+357

Symposium - International Astronomical Union ◽

10.1017/s0074180900080244 ◽

1996 ◽

Vol 175 ◽

pp. 115-117

Author(s):

R. W. Porcas ◽

A. R. Patnaik

Keyword(s):

Time Delay ◽

Mass Distribution ◽

Hubble Constant ◽

Gravitational Lens ◽

Radio Sources ◽

Constant Independent ◽

Lens System ◽

Vlbi Observations ◽

Spectrum Radio ◽

Simple Mass

The gravitational lens system B0218+357 comprises 2 image components (A and B) and a radio ‘Einstein Ring’ (Patnaik et al, 1993). The redshift of the lens galaxy is 0.6847 (Browne et al, 1994) and that of the imaged source 0.96 (preliminary result; Lawrence et al, 1995). The separation of A and B, which are both flat-spectrum radio sources, is only 0.335 arcsec, leading to the hope that the lens is a single galaxy with a relatively simple mass distribution. Refsdal pointed out (1964) that a model of such a distribution, and a measurement of the time difference along the two image paths, leads to an estimate of the Hubble constant, independent of the usual steps in the distance ladder. B0218+357 is one of only a few lensed systems well suited for such measurements. A preliminary value of 12 days has been measured for the A-B time delay, derived from a comparison of the percentage polarisation variations of the images at 15GHz, using the VLA (Corbett et al, 1995).

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VLBI Observations of the 0957+561 Gravitational Lens System

Symposium - International Astronomical Union ◽

10.1017/s0074180900134473 ◽

1988 ◽

Vol 129 ◽

pp. 201-206

Author(s):

M. V. Gorenstein ◽

R. J. Bonometti ◽

N. L. Cohen ◽

E. E. Falco ◽

I. I. Shapiro ◽

...

Keyword(s):

Time Delay ◽

Flux Density ◽

Gravitational Lens ◽

Time Variability ◽

Lens System ◽

Relative Time ◽

Vlbi Observations ◽

New Information ◽

Superluminal Motion ◽

Upper Limits

A series of VLBI observations of the gravitational lens system 0957+561 at λ13 cm has yielded the positions of the A and B images, the relative magnification of their largest discernible radio structures, and the time variability of their smallest discernible radio structures. These observations have also allowed upper limits to be placed on the flux density of an expected third image. The positions and relative magnification of the A and B images provide new information with which to constrain models of the lens that forms the images. The detection of variations in the flux densities of the cores of A and B suggests that observations at shorter wavelengths may reveal superluminal motion, which may in turn provide a means to measure the relative time delay.

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VLBI Observations of the Gravitational-Lens Images of Q0957+561

Symposium - International Astronomical Union ◽

10.1017/s0074180900078153 ◽

1984 ◽

Vol 110 ◽

pp. 243-246

Author(s):

M. V. Gorenstein ◽

I. I. Shapiro ◽

N. L. Cohen ◽

R. J. Bonometti ◽

E. E. Falco ◽

...

Keyword(s):

Time Delay ◽

Data Acquisition ◽

Mass Distribution ◽

Data Acquisition System ◽

Gravitational Lens ◽

Acquisition System ◽

Vlbi Observations ◽

Vlbi Data ◽

Cosmological Constants

We have conducted a series of VLBI observations of the gravitational-lens images of the quasar Q0957+561 (Walsh et al., 1979), utilizing the Mark III VLBI data acquisition system (Rogers et al., 1983). The goals of our observations are to (1) map the milliarcsecond structure of the A and B images, (2) detect the predicted third image of the quasar, and (3) determine the time delay between the images. We will use these results to constrain the mass distribution of the lens and, possibly, cosmological constants.

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Multi-Frequency VLBI Observations Of B0218+357

Symposium - International Astronomical Union ◽

10.1017/s0074180900231665 ◽

1996 ◽

Vol 173 ◽

pp. 311-316

Author(s):

Richard W. Porcas ◽

Alok R. Patnaik

Keyword(s):

Mass Distribution ◽

Gravitational Lens ◽

Lens System ◽

Double Structure ◽

Vlbi Observations ◽

The Matrix ◽

5 Ghz

We present the results from VLBI observations at three frequencies of the gravitational lens system B0218+357. From the source double structure, seen in both the A and B images at 15 GHz, we have derived a relative magnification matrix, and we show that the lens mass distribution must be non-spherical. We investigate how far the matrix parameters derived from 15 GHz observations can be used to relate the A and B images at 1.7 and 5 GHz, where the image sizes are much larger.

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VLBI Observations of Gravitational Lens Systems

Symposium - International Astronomical Union ◽

10.1017/s0074180900134461 ◽

1988 ◽

Vol 129 ◽

pp. 191-199

Author(s):

Edwin L. Turner

Keyword(s):

Gravitational Lens ◽

Lens System ◽

Additional Test ◽

System A ◽

Vlbi Observations ◽

Vlbi Data ◽

Cosmological Tests ◽

Superluminal Expansion ◽

Additional Constraints

Four specific and particularly powerful types of possible VLBI lens studies are discussed. First, comparison of mas scale structure in putative pairs of images separated by arc seconds can provide a powerful additional test of the lens hypothesis in specific candidate systems. Second, VLBI searches for lens systems with image separations too small for resolution by optical or VLA searches will limit (or even determine!) the cosmological density of condensed objects with individual masses ∼ 106M⊙. Third, study of multiply imaged superluminal expansion events will allow a determination of the light travel time delay between different images in a lens system, a quantity which is quite difficult to measure by other means but which would allow profound cosmological tests. Fourth, VLBI data can be used to determine relative image parities and even the full magnification matrix of various images in a lens system, thus providing powerful additional constraints on detailed lens models. Finally, the speculative possibility of detecting Galactic stellar lensing events using VLBI techniques is discussed.

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