user: For the abstract "ABSTRACT
We measure the size-luminosity relation of photometrically-selected galaxies within the redshift
range 𝑧  6 􀀀 9, using galaxies lensed by six foreground Hubble Frontier Fields (HFF)
clusters. The power afforded by strong gravitational lensing allows us to observe fainter and
smaller galaxies than in blank fields. We select our sample of galaxies and obtain their properties,
e.g., redshift, magnitude, from the photometrically-derived ASTRODEEP catalogues.
The intrinsic size is measured with the Lenstruction software, and completeness maps
are created as a function of size and luminosity via the GLACiAR2 software. We perform a
Bayesian analysis to estimate the intrinsic and incompleteness-corrected size-luminosity distribution,
with parameterization 𝑟𝑒 / 𝐿𝛽. We find slopes of 𝛽  048  008 at 𝑧  6 􀀀 7
and 𝛽  068  014 at 𝑧  85, adopting the Bradac lens model. The slope derived by lensed
galaxies is steeper than that obtained in blank fields and is consistent with other independent
determinations of the size-luminosity relation from the HFF dataset. We also investigate the
systematic uncertainties correlated with the choice of lens models, finding that the slopes of
size-luminosity relations derived from different models are consistent with each other, i.e. the
modeling errors are not a significant source of uncertainty in the size-luminosity relation." list the findings, methodology and purpose in a table

assistant: | Aspect      | Summary                                                                                                                                                                                                  |
|-------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| Findings    | - Measure the size-luminosity relation of photometrically-selected galaxies within the redshift range of 6 to 9.                                                                                         |
|             | - Find steeper slopes of the size-luminosity relation for lensed galaxies compared to blank fields, and consistent with other independent determinations from the HFF dataset.                           |
|             | - Investigate the systematic uncertainties correlated with the choice of lens models, finding that the modeling errors are not a significant source of uncertainty.                                      |
| Methodology | - Use galaxies lensed by six foreground Hubble Frontier Fields (HFF) clusters.                                                                                                                           |
|             | - Obtain properties of sample galaxies from the photometrically-derived ASTRODEEP catalogues.                                                                                                            |
|             | - Measure intrinsic size with the Lenstruction software.                                                                                                                                                 |
|             | - Create completeness maps as a function of size and luminosity via the GLACiAR2 software.                                                                                                               |
|             | - Perform a Bayesian analysis to estimate the intrinsic and incompleteness-corrected size-luminosity distribution.                                                                                       |
| Purpose     | To measure and analyze the size-luminosity relation of galaxies within the redshift range of 6 to 9, using lensed galaxies and to investigate the systematic uncertainties in the choice of lens models. |

user: Thank you.

assistant: You are welcome. Anything else i can help you with?