Measuring accretion disk sizes of lensed quasars with microlensing time delay in multi-band light curves

Chan, J. H. H.; Rojas, Karina; Millon, M.; Courbin, F.; Bonvin, V.; Jauffret, G.

doi:10.1051/0004-6361/202038971

Cited by 19 publications

(12 citation statements)

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“…Choosing a shallower Chabrier IMF instead of the steeper Salpeter one used here leads to fewer low-mass microlenses and therefore reduces any effect of high-frequency variability. Although this has been shown to affect magnification map properties (see Chan et al 2021), our goal here is to understand such short-timescale variability and therefore we use the Salpeter IMF for all values of M .…”

Section: Resultsmentioning

confidence: 99%

“…We then use a Salpeter initial mass function (IMF) to describe the stellar mass distribution around a given mean stellar mass M . The maps are generated with the GPU-D software, which implements the direct inverse ray-shooting method as described in Vernardos et al (2015), used in other microlensing studies as well (e.g., Chan et al 2021).…”

Section: Microlensing Variabilitymentioning

confidence: 99%

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Constraining quasar structure using high-frequency microlensing variations and continuum reverberation

Paic

Vernardos

Sluse³

et al. 2022

A&A

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Gravitational microlensing is a powerful tool for probing the inner structure of strongly lensed quasars and for constraining parameters of the stellar mass function of lens galaxies. This is achieved by analysing microlensing light curves between the multiple images of strongly lensed quasars and accounting for the effects of three main variable components: (1) the continuum flux of the source, (2) microlensing by stars in the lens galaxy, and (3) reverberation of the continuum by the broad line region (BLR). The latter, ignored by state-of-the-art microlensing techniques, can introduce high-frequency variations which we show carry information on the BLR size. We present a new method that includes all these components simultaneously and fits the power spectrum of the data in the Fourier space rather than the observed light curve itself. In this new framework, we analyse COSMOGRAIL light curves of the two-image system QJ 0158-4325 known to display high-frequency variations. Using exclusively the low-frequency part of the power spectrum, our constraint on the accretion disk radius agrees with the thin-disk model estimate and the results of previous work where the microlensing light curves were fit in real space. However, if we also take into account the high-frequency variations, the data favour significantly smaller disk sizes than previous microlensing measurements. In this case, our results are only in agreement with the thin-disk model prediction only if we assume very low mean masses for the microlens population, i.e. ⟨M⟩ = 0.01 M⊙. At the same time, including the differentially microlensed continuum reverberation by the BLR successfully explains the high frequencies without requiring such low-mass microlenses. This allows us to measure, for the first time, the size of the BLR using single-band photometric monitoring; we obtain RBLR = 1.6−0.8+1.5 × 1017 cm, in good agreement with estimates using the BLR size–luminosity relation.

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Section: Resultsmentioning

confidence: 99%

Section: Microlensing Variabilitymentioning

confidence: 99%

Constraining quasar structure using high-frequency microlensing variations and continuum reverberation

Paic

Vernardos

Sluse³

et al. 2022

A&A

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“…We follow the simulation technique in Chen et al (2018), which itself is built on the approach in Kochanek (2004) to compute microlens tracks. The technique is implemented in the code GPU-D 45 (Vernardos & Fluke 2014), further modified by Chan et al (2021) to account for the initial mass function (IMF). For the population of lenses we assume a Salpeter (Salpeter 1955) IMF and a mean solar mass of 0.3 M ☉ .…”

Section: Appendix a Sie+γ Modelmentioning

confidence: 99%

A Highly Magnified Gravitationally Lensed Red QSO at z = 2.5 with a Significant Flux Ratio Anomaly

Glikman

Rusu

Chen

et al. 2023

ApJ

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We present the discovery of a gravitationally lensed dust-reddened QSO at z = 2.517, identified in a survey for QSOs by infrared selection. Hubble Space Telescope imaging reveals a quadruply lensed system in a cusp configuration, with a maximum image separation of ∼1.″8. We find that, compared to the central image of the cusp, the neighboring brightest image is anomalous by a factor of ∼7–10, which is the largest flux anomaly measured to date in a lensed QSO. Incorporating high-resolution Very Large Array radio imaging and submillimeter imaging with the Atacama Large Millimeter/submillimeter Array, we conclude that a low-mass perturber is the most likely explanation for the anomaly. The optical through near-infrared spectrum reveals that the QSO is moderately reddened with E(B − V) ≃ 0.7–0.9. We see an upturn in the ultraviolet spectrum due to ∼1% of the intrinsic emission being leaked back into the line of sight, which suggests that the reddening is intrinsic and not due to the lens. The QSO may have an Eddington ratio as high as L/L Edd ≈ 0.2. Consistent with previous red QSO samples, this source exhibits outflows in its spectrum, as well as morphological properties suggestive of it being in a merger-driven transitional phase. We find a host galaxy stellar mass of log M ⋆ / M ⊙ = 11.4 , which is higher than the local M BH versus M ⋆ relation but consistent with other high-redshift QSOs. When demagnified, this QSO is at the knee of the luminosity function, allowing for the detailed study of a more typical moderate-luminosity infrared-selected QSO at high redshift.

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“…Further, our maps have a resolution of 20000 × 20000 pixels with a total size of 20 R Ein × 20 R Ein , where the Einstein Radius R Ein is a characteristic size of the map which depends on the source redshift z s , lens redshift z d , and masses of the microlenses. As in Huber et al (2020), we follow Chan et al (2021) for generating the microlensing magnification maps and assume a Salpeter initial mass function (IMF) with a mean mass of the microlenses of 0.35M ; the specifics of the assumed IMF have negligible impact on our studies. From the flux we obtain the AB-magnitudes via…”

Section: Microlensing and Sne Ia Modelsmentioning

confidence: 99%

HOLISMOKES -- VII. Time-delay measurement of strongly lensed Type Ia supernovae using machine learning

Huber,

Suyu,

Ghoshdastidar

et al. 2021

Preprint

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The Hubble constant (H 0 ) is one of the fundamental parameters in cosmology, but there is a heated debate on the >4σ tension between the local Cepheid distance ladder and the early Universe measurements. Strongly lensed Type Ia supernovae (LSNe Ia) are an independent and direct way to measure H 0 , where a time-delay measurement between the multiple supernova (SN) images is required. In this work, we present two machine learning approaches to measure time delays in LSNe Ia, namely, a fully connected neural network (FCNN) and a Random Forest (RF). For the training of the FCNN and the RF, we simulate mock LSNe Ia from theoretical SN Ia models including observational noise and microlensing. We test the transfer learning capability of both machine learning models, by using a final test set based on empirical LSN Ia light curves not used in the training process, and we find that only the RF provides low enough bias to achieve precision cosmology, which is therefore preferred to our FCNN approach for applications to real systems. For the RF with single-band photometry in the i-band, we obtain an accuracy better than 1% in all investigated cases for time delays longer than 15 days, assuming follow-up observations with a 5σ point-source depth of 24.7, a two day cadence with a few random gaps and a detection of the LSNe Ia 8 to 10 days before peak in the observer frame. In terms of precision, we can achieve under the same assumptions on the i band ∼1.5 days uncertainty for a typical source redshift of ∼0.8. To improve the measurement we find that three bands, where we train a RF for each band separately and combine them afterwards, help to reduce the uncertainty to ∼1.0 day. The dominant source of uncertainty is the observational noise and therefore the depth is an especially important factor when follow-up observations are triggered.

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Measuring accretion disk sizes of lensed quasars with microlensing time delay in multi-band light curves

Cited by 19 publications

References 58 publications

Constraining quasar structure using high-frequency microlensing variations and continuum reverberation

Constraining quasar structure using high-frequency microlensing variations and continuum reverberation

A Highly Magnified Gravitationally Lensed Red QSO at z = 2.5 with a Significant Flux Ratio Anomaly

HOLISMOKES -- VII. Time-delay measurement of strongly lensed Type Ia supernovae using machine learning

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