A STUDY OF GRAVITATIONAL LENS CHROMATICITY WITH THE HUBBLE SPACE TELESCOPE^*

HE 0512−3329 is a two-image lensed quasar with a separation of 065 and a source redshift of z_s = 1.565 (Gregg et al. 2000). The lens redshift is not directly measured, but the presence of a damped Lyα absorber (DLA) system and associated strong metal line absorption systems suggests that the lens is a spiral galaxy at z_l = 0.93 (Gregg et al. 2000; Wucknitz et al. 2003). Table 2 presents the photometry for the lens galaxy as well as the quasar images in the CASTLES data. While the time delays are not measured, they will be so short given the image separation (∼10 days is estimated from a singular isothermal ellipsoid model) that the single epoch flux ratios will be unaffected by intrinsic variability.

As we see in Figure 2, the flux ratios have a steep dependence on the wavelength, and the slope is little changed from the earlier CASTLES results or the later results from Eliasdottir et al. (2006). While there are offsets between the epochs indicative of microlensing, they show no significant wavelength dependencies. Wucknitz et al. (2003) found that the broad emission line flux ratios, which should be very little affected by microlensing, show a wavelength dependence consistent with these trends. They also found evidence of microlensing in the continuum.

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Figure 3 shows the result of fitting the flux ratios assuming they are due to differential extinction. Like Wucknitz et al. (2003), and unlike Eliasdottir et al. (2006), we identify a weak 2175 Å feature. The Galactic CCM extinction curve fits poorly, with χ² = 13 for 4 degrees of freedom (dof), an estimated R(V) ≲ 0.5, and a best-fit R(V) ≃ 0, a region where the model makes no sense. The model with the weaker feature of the mean SMC extinction law fits far better, with χ² = 2.8 for 5 dof and ΔE(B − V) = 0.06 ± 0.01. If we allow the parameter responsible for the stretch of the bump (c3) in the FM extinction law to vary, we find a best fit with χ² = 1.1 for 4 dof and parameter c3 = 1.7 ± 0.9 confirming the marginal detection of the bump by Wucknitz et al. (2003). The interpretation of the flux ratios as extinction and the feature as the 2175 Å feature seems robust since we obtain a dust redshift of z_d = 0.92 ± 0.15 that is in good agreement with that of the DLA and metal line systems at z_l = 0.93 (Gregg et al. 2000; Wucknitz et al. 2003). Although 25% of the C iv emission line lies in the F435W filter, we estimate that differential microlensing between the line and continuum of order 0.2 mag would lead to a line-induced bias in the estimated continuum flux ratios of only ∼0.01 mag. This is smaller than the photometric uncertainties and cannot explain the observed shift of ≃ 0.1 mag.

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B 1600+434 is a two-image system with a separation of 14, a source redshift of z_s = 1.59, and a lens redshift of z_l = 0.41 (Jackson et al. 1995) where the lens is a nearly edge-on spiral (Jaunsen & Hjorth 1997). The time delay is relatively short (∼47 days; Koopmans et al. 2000; Burud et al. 2000), so single epoch flux ratios will be little affected by intrinsic variability. Not surprisingly, it was quickly found that the image passing through the disk of the galaxy suffered from extinction (Jaunsen & Hjorth 1997; Falco et al. 1999; Burud et al. 2000).

Figure 4 shows the magnitude differences as a function of wavelength, where the redder image A is the image passing through the disk of the lens. The slope of the differences is little changed from the CASTLES observations, but there is an offset of approximately 0.3 mag. Thus, as for HE 0512−3329, the dominant effect is differential extinction with weaker effects due to microlensing that show no obvious wavelength dependence. Figure 5 shows a fit to the flux ratios assuming they are due to extinction, where we have used the 6 cm radio flux ratio (Koopmans et al. 2000) as an extinction-free anchor for the ratios. The data are well fit by a CCM extinction law with R(V) = 1.5 ± 0.3 and ΔE(B − V) = 0.39 ± 0.02. The structure of the extinction law is not tightly constrained because the 2175 Å feature is not only blueward of our shortest wavelength filter but also lies on top of the Lyα line of the quasar. Dai & Kochanek (2005) estimated a gas column density difference between the images of ∼3 × 10²¹ cm⁻² based on differences in the X-ray spectra of the two images. Using the extinction estimate of ΔE(B − V) ≃ 0.1 from Falco et al. (1999), this implied a dust-to-gas ratio that was somewhat high. However, if we adopt our new estimate, we find a dust-to-gas ratio of ∼7 × 10²¹ mag⁻¹ cm⁻² that is very close to the typical Galactic value of 5.8 × 10²¹ mag⁻¹ cm⁻² (Bohlin et al. 1978).

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H 1413+117 is a four image system with a maximum separation of ∼11 and z_s = 2.55 (Magain et al. 1988). The lens galaxy is marginally detected in the H band and its redshift is unknown, although Kneib et al. (1998) propose z ∼ 0.9 based on the photometric redshifts of nearby galaxies. Figure 6 shows the magnitude differences for our HRC observations, the CASTLES data, the Turnshek et al. (1997) and Chae et al. (2001) data, and the mid-infrared (11 μm) flux ratios from MacLeod et al. (2009). The small shifts between the epochs appear to be due to changes in the fluxes of images A and D, at levels of approximately 0.1 and 0.05 mag. The largest wavelength dependencies correspond to images A and B and the lack of significant changes in the colors with time indicates that they should be attributed to extinction. The lack of a wavelength dependence between images D and C suggests that they are little affected by either extinction or chromatic microlensing at these wavelengths. The small bump in the F435W magnitude differences including image D (see Figure 6) is probably due to contamination by the Lyα emission line. In Figure 6, we also see that the flux ratios excluding image D (m_A − m_C, m_B − m_C) extend naturally into the mid-IR as might be expected for extinction, while the flux rations including image D (m_B − m_D, m_D − m_C) show significant shifts (∼0.2 mag) going from near-IR to the mid-IR. This seems more easily explained by microlensing, where the near-IR emission is from the accretion disk while the mid-IR emission is from thermal dust emission on larger scales. Recently, Hutsemékers et al. (2010) have reached similar conclusions based on spectroscopic differences between the images.

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We conclude that A and B images are significantly affected by differential extinction from the lens galaxy. Unfortunately, the lack of a candidate for the 2175 Å feature combined with the unknown redshift of the lens galaxy makes it difficult to analyze the extinction. If the bump feature is present in the lens galaxy, its absence in our observations implies a very low lens redshift (≲ 0.3), as illustrated by the example for a lens at z_l = 0.25 shown in Figure 7. The failure to detect the lens in the V- and I-band HST observations almost certainly guarantees that the lens redshift cannot be so low. Thus, we must conclude that the extinction law in this lens lacks a significant 2175 Å feature.

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HE 1104−1805 is a two-image lensed quasar with a relatively large separation of ∼32, a source redshift of z_s = 2.32 (Wisotzki et al. 1993), and a lens redshift of z_l = 0.73 (Lidman et al. 2000). Lehár et al. (2000) modeled the system in detail using the CASTLES images. The time delay is relatively long (∼162 days; Morgan et al. 2008), but based on the statistics of quasar variability discussed in Section 2, our single epoch flux ratios should not be strongly biased. Falco et al. (1999) modeled the flux ratios as extinction, although the X-ray absorption study by Dai et al. (2006) found negligible differential absorption. In fact, it was also clear from the later light curves (Schechter et al. 2003; Poindexter et al. 2007) that there was significant chromatic microlensing in this system. Indeed, as Poindexter et al. (2008) noted in their detailed study of microlensing, the relative colors of the two images reversed over the period since its discovery, very different from the limited color changes seen in the first three lenses we considered. Further evidence against significant extinction is that the mid-IR flux ratios from Poindexter et al. (2007) agree well with the emission line flux ratios (Wisotzki et al. 1993). Figure 8 shows the magnitude differences for images A and B for each ACS/HRC filter, along with the CASTLES magnitude differences and the mid-IR flux ratios from Poindexter et al. (2007). We can see again the change in slope of the wavelength dependence between the two epochs indicating the detection of chromatic microlensing.

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We separately modeled the two epochs of HST observations using the procedures from Mediavilla et al. (2011) and Mosquera et al. (2011), as briefly outlined in Section 2, to compare the results from single epoch models to the more complex light curve modeling procedures used by Poindexter et al. (2008). Figure 9 shows the estimates for the scale radius r_s in the F336W filter (1013 Å in the rest frame) and the logarithmic slope p of the size with wavelength, r_s∝λ^p, for the HRC data, the CASTLES data, and the combination of the two assuming either a logarithmic or a linear prior on r_s. In thin disk theory, where the disk temperature profile is T∝R^−3/4, we would expect to find p = 4/3. Given the nature of the chromatic microlensing detected in the HRC observations the uncertainties are substantially greater than the ones derived from the CASTLES data, with its steeper, monotonic variations in the flux ratios, but the estimates (see Table 4) agree within the uncertainties. When we combine the two results, we find p = 1.1 ± 0.6 and r_s = 4⁺⁴_{− 2} lt-day for the logarithmic prior on the size, and p = 1.0 ± 0.6 and r_s = 7 ± 4 lt-day for the linear prior. We can compare to Poindexter et al. (2008), who used a different disk model and normalizing wavelength, by converting the scale lengths to the half-light radii R_1/2 of the models since Mortonson et al. (2005) showed that different microlensing models will agree on the half-light radius of the distribution. We transform our r_s at λ = 3363 Å to R_1/2(λ4311) = 1.18 (4311/3363)^p r_s(λ3363) at the normalizing wavelength λ = 4311 Å used by Poindexter et al. (2008). In addition we rescale our microlens mass to M = 0.3 M_☉ from M = 1 M_☉ ($r_s\propto \sqrt{M}$) as this is closer to the expectation for normal stellar populations (see Poindexter et al. 2008). Figure 10 shows that our combined results are in excellent agreement with those of Poindexter et al. (2008). These estimated sizes of R_1/2 ∼ 9(16) × 10¹⁵ cm for the logarithmic (linear) prior imply, assuming a simple thin disk model (p = 4/3) radiating at the Eddington limit with 10% efficiency, a mass for the central black hole of M_BH ∼ 4.6(10) × 10⁹ M_☉ which agrees well with estimates from emission line widths of M_BH = 2⁺³_{− 1} × 10⁹ M_☉ from Assef et al. (2011). Thus, the quasar accretion disk is larger than the gravitational radius r_g = GM_BH/c², R_1/2 ∼ 13(10)r_g, and smaller than the Einstein radius in the source plane r_E, R_1/2 ∼ 0.4(0.2)r_E, for the logarithmic (linear) prior.

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FBQ 0951+2635 is a two-image lens with an image separation of 11, a source redshift of z_s = 1.24 (Schechter et al. 1998), and a lens redshift of z_l = 0.260  ±  0.002 (Eigenbrod et al. 2007). The time delay is short, ∼16 days (Jakobsson et al. 2005), and several studies have detected microlensing variability at the level of 0.04 mag year⁻¹ (e.g., Schechter et al. 1998; Jakobsson et al. 2005; Paraficz et al. 2006). Figure 11 shows our measurements of the magnitude differences between the two images along with the differences found by CASTLES. The magnitudes of the differences are smaller than in the previous four systems, and it is clear that there is little differential extinction. This agrees with the similar conclusion of Mosquera et al. (2011) based on ground-based narrowband imaging. The UV data from HST allow us to cover the wavelength range where the 2175 Å feature is expected given the measured redshift of the lens galaxy. Although we see a small feature in the F250W filter, we cannot simply attribute it to the 2175 Å bump because it also overlaps the Lyα emission line of the quasar. The differences between the present data and the CASTLES observations indicate the presence of chromatic microlensing, but the amplitudes are too small for single epoch microlensing models to yield significant results. Nonetheless, we confirm that FBQ 0951+2635 is a good candidate for future measurements, reinforced by the fact that Morgan et al. (2010) were already able to estimate a disk size based on microlensing variability in the R-band light curves of this source.

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SBS 1520+530 is a two-image lens with an image separation of ≃ 16, a source redshift of z_s = 1.86, and a lens redshift of z_l = 0.72 (Chavushyan et al. 1997). Burud et al. (2002) measured a time delay for the system of ∼130 days, and Gaynullina et al. (2005) and Paraficz et al. (2006) observed microlensing at a level of ∼0.14 mag over roughly four years. Morgan et al. (2010) estimated an R-band half-light radius for the disk based on modeling these light curves. Unfortunately, our HRC observations do not show a significant chromaticity signal to allow us to perform a deeper analysis. Figure 12 shows the magnitude differences as a function of wavelength for our HRC data and the CASTLES differences presented in Table 2. The wavelength-dependent trends in the ACS/HRC observations are weak, indicating that the differential extinction is very low. Interpreting the CASTLES data is difficult because the V-band (F555W) flux ratio has an unexpected value with a large error bar. We have inspected the CASTLES data several times and have been unable to find a systematic problem (e.g., missed cosmic rays) that would explain the discrepancy.

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