• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Constraining the Temperature-density Relation of the Inter-galactic Medium from Analytically Modeling Lyα Forest Absorbers

    2023-05-29 10:28:00LiYangZhengZhengandKim

    Li Yang , Zheng Zheng, and T.-S.Kim

    1 Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China; liyang@shao.ac.cn

    2 School of Astronomy and Space Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

    3 Department of Physics and Astronomy, University of Utah, 115 S 1400 E, Salt Lake City, UT 84112, USA; zhengzheng@astro.utah.edu

    4 Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI 53706, USA

    Abstract The absorption by neutral hydrogen in the intergalactic medium (IGM) produces the Lyα forest in the spectra of quasars.The Lyα forest absorbers have a broad distribution of neutral hydrogen column density NH I and Doppler b parameter.The narrowest Lyα absorption lines (of lowest b) with neutral hydrogen column density above~1013cm-2 are dominated by thermal broadening, which can be used to constrain the thermal state of the IGM.Here we constrain the temperature-density relation T = T0 (ρ ρˉ)γ -1of the IGM at 1.6 <z <3.6 by using NH I and b parameters measured from 24 high-resolution and high-signal-to-noise quasar spectra and by employing an analytic model to model the NH I-dependent low-b cutoff in the b distribution.In each NH I bin, the b cutoff is estimated using two methods, one non-parametric method from computing the cumulative b distribution and a parametric method from fitting the full b distribution.We find that the IGM temperature T0 at the mean gas density ρˉ shows a peak of ~1.5×104 K at z ~2.7–2.9.At redshift higher than this, the index γ approximately remains constant, and it starts to increase toward lower redshifts.The evolution in both parameters is in good agreement with constraints from completely different approaches, which signals that He II reionization completes around z ~3.

    Key words: (galaxies:) intergalactic medium – (galaxies:) quasars: absorption lines – radiation mechanisms:thermal

    1.Introduction

    The Lyman-α (Lyα) forest, namely the ensemble of absorption lines blueward of the Lyα emission in the spectra of the quasar,is caused by the absorption of intervening neutral hydrogen in the intergalactic medium (IGM) (e.g., Cen et al.1994; Bi & Davidsen 1997; Rauch 1998).As the largest reservoir of baryons, the evolution of the IGM is affected by several processes, such as adiabatic cooling caused by cosmic expansion, heating by ionizing photons from galaxies and quasars, and heating from gravitational collapse.The Lyα forest encodes the thermal state of the IGM (Gunn &Peterson 1965; Lynds 1971; Hui & Gnedin 1997; Schaye et al.1999, 2000) and therefore it has become the premier probe of the thermal and ionization history of the IGM.

    The thermal state of the IGM is usually characterized by the temperature-density relation, parameterized as T=T0Δγ-1(Hui & Gnedin 1997).Here,ρ ρΔ ≡ ˉ is the ratio of the gas density to its cosmic mean,the normalization T0corresponds to the temperature of the gas at the mean density, and γ denotes the slope of the relation.Measuring T0and γ as a function of redshift would allow the reconstruction of the thermal and ionization history of the IGM.In particular,the H I reionization and He II reionization leave distinct features in the evolution of T0and γ, and the properties of the Lyα forest contain their imprint(e.g.,Miralda-Escudé&Rees 1994;Theuns et al.2002;Hui & Haiman 2003; Worseck et al.2011; Puchwein et al.2015; Upton Sanderbeck et al.2016; Worseck et al.2016;Gaikwad et al.2019;Worseck et al.2019;Upton Sanderbeck&Bird 2020).Various statistical properties of the Lyα forest have been applied to measure T0and γ, such as the Lyα forest flux power spectrum and the probability distribution of flux(Theuns et al.2000; McDonald et al.2001; Zaldarriaga et al.2001;Bolton et al.2008; Viel et al.2009; Calura et al.2012; Lee et al.2015; Rorai et al.2017; Walther et al.2018; Boera et al.2019; Khaire et al.2019; Walther et al.2019; see Gaikwad et al.2021 for a summary).

    There is also a method of measuring the IGM thermal state based on Voigt profile decomposition of the Lyα forest (e.g.,Schaye et al.1999; Bryan & Machacek 2000; Ricotti et al.2000; Schaye et al.2000; McDonald et al.2001; Rudie et al.2012;Bolton et al.2014;Hiss et al.2018;Rorai et al.2018).In this approach, the Lyα absorption spectrum is treated as a superposition of multiple discrete Voigt profiles,with each line described by three parameters:redshift z,Doppler parameter b,and neutral hydrogen column density NHI.By studying the statistical properties of these parameters, i.e., the b–NHIdistribution at a given redshift, one can recover the thermal information encoded in the absorption profiles.The underlying principle of this approach is that the narrow absorption lines(with low b)are dominated by thermal broadening,determined by the thermal state of the IGM.

    Such an approach involves the determination of the cutoff in the b distribution as a function of NHI.The commonly-used method follows an iterative procedure introduced by Schaye et al.(1999):fit the observed b–NHIdistribution with a power law; discard the data points 1σ above the fit; iterate the procedure until convergence in the fit.With the small number of H I lines around the b cutoff and contamination by noise and metals, different line lists can lead to different results on the T0and γ constraints (e.g., Rudie et al.2012; Hiss et al.2018).

    In this paper, we employ the low-b cutoff profile approach to constrain the IGM thermal state at z ~3.We circumvent the above problem of determining the profile of the b cutoff by proposing two different methods.The first one is a nonparametric method,which measures the lower 10th percentile in the b distribution from the cumulative b distribution in each NHIbin.The other one is a parametric method, which infers the lower 10th percentile in the b distribution from a parametric fit to the full b distribution in each NHIbin.With the determined b cutoff profiles, to derive the constraints on T0and γ, we apply a physically motivated and reasonably calibrated analytic model describing the b cutoff, which avoids using intensive simulations.Unlike previous work(e.g., Schaye et al.1999; Rudie et al.2012; Hiss et al.2018),where the low-b cutoff profile is obtained by iteratively removing data points based on power-law fits, our methods make use of a well-defined NHI-dependent low-b cutoff threshold, i.e., the lower 10th percentile in the b distribution.Adopting such a quantitative cutoff threshold allows a direct comparison to the analytic model of Garzilli et al.(2015)with the same cutoff threshold, providing a simple and efficient way of constraining the thermal state of the IGM.In this paper, we present the methods and apply them for the first time to observed Lyα forest line measurements for T0and γ constraints.

    In Section 2,we describe the data used in this work,which is a list of Lyα absorption lines with Voigt profile measurements from 24 observed high-resolution and high-signal-to-noise(high-S/N) quasar spectra by Kim et al.(2021).In Section 3,we present the overall distribution of NHIand b.Then we present the two methods of determining the b cutoff profile and obtain the constraints on T0and γ in the redshift range of 1.6 <z <3.6.Finally, we summarize our results in Section 4.In the Appendix, we list the constraints in Table A1.

    In this work,we analyze the fitted line parameters of the Lyα forest by Kim et al.(2021): the absorber redshift z, the(logarithmic) neutral hydrogen column density logNHI=log [NHI(c m-2)], and the Doppler parameter

    2.Data Samples and Reduction Methods

    b(km s-1).This list is based on Voigt profile fitting analysis for the 24 high-resolution and high-S/N quasar spectra, taken from HIRES (HIgh-Resolution Echelle Spectrometer; Vogt et al.1994; Vogt 2002) on Keck I and UVES (UV-Visible Echelle Spectrograph; Dekker et al.2000) on the Very Large Telescope (VLT).The resolution is about 6.7 km s-1.The list of quasars and the details of the fitting analysis can be found in Kim et al.(2021).

    The data set from 24 HIRES/UVES quasar spectra in Kim et al.(2021) is unique in combining three aspects of the line fitting analysis: high-S/N (>45 per pixel) to reduce the possibility of misidentifying metal lines as H I absorption lines,without Damped Lyα Absorbers(DLAs)in the spectra to avoid cutting down the available wavelength region significantly and the difficulty in spectra normalization and removal of metals blended with H I, and Voigt profile fitting both from Lyα only and from available Lyman series to more effectively deblend saturated lines.As a comparison, in studying the IGM thermal state, Hiss et al.(2018) use 75 HIRES/UVES spectra at 2.0 <z <3.4 with low S/N (>15 per pixel) containing DLAs,with parameters derived from Lyα-only fit; Gaikwad et al.(2021) use 103 HIRES spectra at 2.0 <z <4.0 with low S/N(>5 per pixel) without DLAs or sub-DLAs, also with parameters derived from Lyα-only fit; Rudie et al.(2012) use 15 HIRES spectra with high S/N (>50 per pixel) containing DLAs, with parameters from fitting both Lyα and Lyβ, but only covering 2 <z <2.8.The line measurements in Kim et al.(2021) from the self-consistent, uniform in-depth Voigt profile fitting analysis with reduced systematics are well suited to our application of testing new methods of studying the IGM around z ~3.

    Figure 1.A portion of the reconstructed Lyα forest spectrum,using NH I and b parameters measured from QSO Q0636+6801 in Kim et al.(2021)either based on the Lyman series fit(left panels)and the Lyα-only fit(right panels).The upper and lower panels show the NH I and b measurements with their uncertainties,respectively,and the middle panels show the normalized flux with short vertical lines indicating the locations of the identified Lyα absorbers.

    We refer interested readers to Kim et al.(2021)for details on the line analysis.As an illustration,Figure 1 shows a portion of the reconstructed Lyα forest spectrum from the line list of one quasar (Q0636+6801), with parameters based on the Lyman series fit (left) and the Lyα-only fit (right).For each set, the reconstructed high-resolution spectrum is shown in the middle panel.As expected, there are no noticeable differences in the reconstructed spectra from the two sets of fitting parameters,since the fitting is performed to reproduce absorption profiles.The small vertical lines in each middle panel mark the locations of individual absorbers, and the dots in the top and bottom panels are the valueslogNHIand b from Voigt fitting for these absorbers, as in the line list from Kim et al.(2021).Note that the uncertainties inlogNHIand b on the left panels are typically smaller, as not only Lyα lines but also all available Lyman series lines are used in deriving these parameters.Lyman series lines of good signal-to-noise ratios also help resolve absorption structures, especially for saturated Lyα absorptions.While this leads to small differences in the exact line lists in the left and right panels, it has little effect on the overall statistical properties of line parameters (Kim et al.2021).

    We will analyze the properties of absorbers from the line list(Kim et al.2021) and use them to constrain T0and γ of the IGM thermal state.

    3.Constraining the Temperature-density Relation from Lyα Absorbers

    3.1.b–NH I Distribution and b Cutoff

    The color-scale maps in Figure 2 show the overall distribution of NHIand b for the full absorber redshift range z ∈[1.6, 3.6] (top) and for z ~3 (z ∈[2.8, 3.2];bottom), based on the line lists from the Lyman series fit (left) and the Lyαonly fit (right), respectively.We exclude lines with b <10 km s-1as they are most likely metal line contaminants or Voigt fit artifacts5.Lines with b >100 km s-1are also excluded as they have a larger contribution from turbulent broadening than from thermal broadening.These extremely broad lines are rare and discarding them does not affect any of our results.To produce each map, we represent the likelihood of each pair of thelogNHIandlogbmeasurement as a bivariate Gaussian distribution using the measurement uncertainties and evaluate the sum of the likelihoods from all the absorbers in grid cells withΔ logNHI=0.2andΔlogb=0.01.The results are shown with a coarser grid.

    The b–NHIdistributions in Figure 2 look similar to each other.The b distribution peaks around 20–30 km s-1, with a slightly higher value at the lower end of the column density.Lyα absorption lines are broadened by both thermal motion and non-thermal broadening resulting from the combination of Hubble flow, peculiar velocities, and turbulence.In many applications (e.g., Schaye et al.1999; Ricotti et al.2000;Schaye et al.2000; McDonald et al.2001; Rudie et al.2012;Boera et al.2014;Bolton et al.2014;Garzilli et al.2015;Hiss et al.2018; Rorai et al.2018; Telikova et al.2021), the narrowest Lyα absorption lines in the Lyα forests are identified and used to constrain the IGM thermal state,as the broadening of these lines is supposed to be purely thermal and the nonthermal broadening is negligible.

    The narrowest Lyα absorption lines define the overall lower cutoff in the b distribution as a function of NHI.We perform such an analysis by computing the locus of the boundary of the lower 10th percentile in the b distribution in each NHIbin.The black points in each panel of Figure 2 delineate such a cutoff boundary, with error bars estimated from bootstrap resampling the data points 100 times.The black solid curve is from an analytic model developed in Garzilli et al.(2015), which describes the minimum line broadening (defined by the 10th percentile cutoff b) as the sum (in quadrature) of the thermal broadening(dotted red line)and the Hubble broadening(dotted blue line).

    The analytic curve is described by Garzilli et al.(2015) as

    Below logNHI~13,the data fall below the model curve.A possible cause is the incompleteness in the data—for low column density absorption systems,those with high values of b would show up as shallow absorption features in the quasar spectrum,which are hard to identify.In Garzilli et al.(2015),a 10th percentile cutoff boundary in the b–NHIdistribution for z ~3 absorbers is presented based on one OWLS simulation(Schaye et al.2010), shown as the empty triangles in each panel of Figure 2.The values of NHIand b are directly computed from the simulation data.Garzilli et al.(2020)further provide the cutoff boundary from Voigt fitting to the simulated Lyα forest spectra (see their Figure A1), which resembles the procedure in analyzing observational data.This is shown as the solid triangles in Figure 2.Compared to the case without Voigt fitting,the cutoff values of b are lowered at the low column density end.That is, at fixed, low column density, Voigt fitting tends to miss shallow absorption lines with high values of b.It is encouraging that our inferred cutoff boundary(shown with black circles)is in good agreement with their simulation-based one from Voigt fitting, including the trend at column density below logNHI~13.

    We make an attempt to use the analytic model developed in Garzilli et al.(2015), i.e., Equations (1)–(4), to constrain the redshift-dependent T0and γ,the two parameters describing the temperature-density relation, T=T0Δγ-1.We first fix fN, fJ,and Γ at their fiducial values as in Equations (1)–(4) and will discuss possible systematic effects introduced by adopting these values.The cosmological parameters(Ωb,Ωm,and h)are also fixed at their fiducial values,which are consistent with the Planck constraints (Planck Collaboration et al.2020).

    We use the 10th percentile cutoff in b for the parameter constraints, as the analytic model is tuned for such a cutoff threshold.Two methods are applied to estimate the 10th percentile cutoff in b in each NHIbin,a non-parametric method that directly measures the 10th percentile from the cumulative b distribution and a parametric method from fitting the full b distribution, as detailed in the following two subsections.

    3.2.T0–γ Constraints from the 10th Percentile b Cutoff Estimated from a Non-parametric Method

    We first present the results based on the 10th percentile cutoff profile estimated using a non-parametric method.Similar to those done in Section 3.1 and in Figure 2,at a given redshift,in eachlogNHIbin, we derive the 10th percentile cutoff boundary of b by computing the cumulative distribution function of b, where each b measurement is taken as a Gaussian distribution with the standard deviation set by the observational uncertainty.The uncertainty in the 10th percentile locus is estimated through bootstrap resampling the data points 100 times.The analytic model is then applied to constrain T0and γ.

    The results are shown in the top two panels of Figure 3(labeled as “10th percentiles”), and T0and γ constraints as a function of z are found in Table A1.The red and blue points are based on b-NHIparameters measured through the Lyman series fit and the Lyα-only fit, respectively.They appear to be consistent with each other, typically within 1σ.Compared to those based on the Lyα-only fit, those based on the Lyman series fit have larger uncertainties at lower redshifts, since the number of available sightlines for the Lyman series fit is smaller.

    Both the values of T0and γ show a clear trend with redshift,with a transition around z ~2.8.The temperature T0at mean density increases from ~104K at z ~1.7 to ~1.55×104K at z ~2.7, then decreases toward higher redshifts, reaching~1.15×104K at z ~3.5.The T0value at z ~3.1 for the Lyman series fit case and that at z ~3.3 for the Lyα-only fit case deviate the trend of decreasing with increasing redshifts,with T0~1.4–1.5×104K, but they are consistent with being fluctuations.For the values of γ, the broad trend appears to be decreasing from γ ~1.4–1.5 to 1.3 in the redshift range of 1.6 to 2.8–2.9 and then flattened (or maybe slightly increasing)toward higher redshifts.The transitions seen in T0and γ around z ~2.7–2.9 are signatures of He II reionization (e.g., Upton Sanderbeck et al.2016; Worseck et al.2019; Villasenor et al.2022).Photons ionizing He II heat the IGM, and the temperature T0climbs up, reaches a peak, and then drops when adiabatic expansion starts to dominate the temperature evolution.Heating the IGM makes γ decrease (e.g., γ would become unity if the IGM is heated to be isothermal)and then it increases when the effect of adiabatic expansion kicks in.

    The temperature-density relation has been observationally constrained with various methods.Early constraints show large scatters and have large uncertainties.We choose to compare to a few recent constraints.As a comparison, the gray squares in the top panels of Figure 3 are from Hiss et al.(2018).They are also constrained through the low-b boundary of the b-NHIdistribution with high-resolution spectra,but by comparing to a set of hydrodynamic simulations.The overall trend is similar to ours,e.g.,a peak in T0at z ~2.8.The variation amplitude in T0from Hiss et al.(2018)appears higher than ours—while the T0values at the low- and high-redshift ends are consistent with ours, their peak T0value is much higher, ~2×104K, ~25%higher than ours(1.55×104K).Similarly,the value of γ from their constraints has a steeper drop from z ~2 to z ~2.9 (with larger uncertainties though).

    Villasenor et al.(2022) constrain the temperature-density relation and the evolution of the ionization rate by fitting the Lyα forest power spectrum from high-resolution spectroscopic observations using a large set of hydrodynamic simulations.The black curves in the top panels show T0and γ constraints from their best fit model, with the shaded bands representing the 1σ uncertainty (very narrow in the γ constraints).Our results agree well with theirs in terms of the variation amplitude of T0, while the peak in our results occurs at a lower redshift(z ~2.7)than theirs(z ~3.0).The trends in γ are also similar to our results showing a slightly lower (higher) γ at low (high)redshifts.Given the uncertainties in our inferred γ values, our results are consistent with theirs.

    The yellow data points are constraints from Gaikwad et al.(2021), based on four different flux distribution statistics of Lyα forests in high-resolution and high-S/N quasar spectra.Accounting for the uncertainties, our results show a good agreement with theirs.

    The green curve in each panel represents the prediction from a hydrodynamic simulation in Upton Sanderbeck et al.(2016),which includes the effect of He II reionization.It almost falls on top of the constraints in Villasenor et al.(2022) for T0.It appears to be slightly lower in γ,but with a quite similar trend.The broad features predicted from this hydrodynamic simulation are similar to our results, except for the small shift in the redshift of the peak T0.

    3.3.T0–γ Constraints from the 10th Percentile b Cutoff Estimated from a Parametric Fit to the b Distribution

    Estimating the b cutoff directly from the cumulative b distribution, while straightforward, can have limitations.First,the IGM thermal state impacts all the lines, not just the narrowest lines.Therefore, by restricting the use of the data in the tail of the distribution near the cutoff,this approach throws away information, which can significantly reduce the sensitivity to the IGM thermal state.Second, in practice, determining the location of the cutoff is vulnerable to systematic effects,such as contamination from unidentified metal lines or misidentified metal lines as H I and noise.

    To overcome these limitations, we develop an approach to infer the 10th percentile b cutoff by a parametric fit to the full b distribution in each NHIbin.To describe the b distribution,we adopt the functional form suggested by Hui&Rutledge(1999),derived based on the Gaussian random density and velocity field.It is a single-parameter distribution function,

    Such a distribution function naturally explains the salient features of the observed b distribution: a sharp low-b cutoff,corresponding to narrow and high amplitude absorptions(statistically rare, related to the tail of the Gaussian distribution), and a long power-law tail toward high b, coming from broad and low-amplitude absorptions.The parameter bσmarks the transition from the exponential cutoff to the power-law part.With this distribution, the b value for the lower 10 percentile cutoff isbσ(l n 10)14.

    For every redshift bin, in each NHIbin, with the observed values of b,we derive the constraints on bσusing the maximum likelihood method6We adopt the publicly available Python Package kafe2 (https://github.com/PhiLFitters/kafe2) to perform the maximum likelihood estimation..The inferred values of the 10th percentile cutoffσbln 1014( ) as a function of NHIare used to constrain T0and γ,as in Section 3.2.The results are shown in the bottom panels of Figure 3 (labeled as “b σ(l n 10)14”).The constraints on T0are similar to those inferred from using the 10th percentile b cutoff estimated from the non-parametric method.The peak is around z ~2.8 with a value of ~1.5×104K.The fluctuation in the trend with redshift is reduced, as expected,given that the 10th percentile boundary is from fitting the overall b distribution.For γ, the trend with redshift is also similar to that based on the non-parametric b cutoff estimate,but the amplitude appears to be lower.The systematic trend may reflect the fact that the analytic model is tuned for the first method, not the second one.However, for most γ values the systematic shifts are within 2σ with the data we use in our analysis.

    Figure 3.Constraints on T0 and γ,the two parameters describing the temperature-density relation T=T0Δγ-1 in the IGM.Our results are shown as open circles,red(blue)circles correspond to Lyα absorber parameters NH I and b measured from the Lyman-series(Lyα-only)fit.In the top panels,our constraints are derived using the b cutoff relation estimated from the data, while those in the bottom panels are from the b cutoff relation inferred from fitting the b distribution.See the text for details.In each panel,The gray squares are constraints from Hiss et al.(2018),also from modeling the b cutoff relation,but with a set of hydrodynamic simulations.The yellow squares are from Gaikwad et al.(2021),constrained based on four different Lyα forest flux statistics.The black curve(with the 95%confidence interval shaded) corresponds to the constraints in Villasenor et al.(2022) by fitting the Lyα forest power spectrum with a large set of hydrodynamic simulations.The green curve is the prediction in Upton Sanderbeck et al.(2016) from a hydrodynamic simulation including the effect of He II reionization.The horizontal line at T0=1.5×104K or γ=1.32 is shown simply as a reference to aid the comparison.

    As a whole, our derived constraints on T0and γ based on two methods of estimating the b cutoff profile broadly agree with each other.They also appear to be consistent with the results inferred by Gaikwad et al.(2021).While the main difference in our two types of constraints lies in the amplitude of γ, both of them appear to be around the Gaikwad et al.(2021) values, typically within 1σ.

    We present the results here as the marginalized constraints on T0and γ,respectively.For completeness,the full constraints with both methods of deriving the b cutoff are shown in the Appendix, where we also provide Table A1 for the T0and γ constraints.

    3.4.Sensitivity of the T0–γ Constraints on Parameters in the Analytic Model

    In obtaining the constraints on T0and γ in Sections 3.2 and 3.3, we have fixed the model parameters fN, fJ, and Γ to their fiducial values in Equations (1)–(4).That is, we neglect their dependence on redshift.One may worry that this could introduce systematic uncertainties in the inferred T0and γ.

    We can study the sensitivity of the T0and γ constraints on these model parameters by considering the low-NHIand high-NHIlimit in the model.At low NHI, where the Hubble broadening dominates, the cutoff in b is approximately

    While the above tests to the sensitivity are general, they do not reflect the expected redshift dependence on the model parameters.For a more realistic assessment of the potential systematics,we turn to simple models of these parameters.The parameter fN, which is the proportionality coefficient relating NHIand the product of the number density nHIand the filtering scale λF=fJλJ, is expected to be insensitive to redshift.The filtering (smoothing) scale λFat a given epoch depends on the history of the Jeans length λJ,i.e.,on the thermal history of the IGM.Therefore, we expect fJto evolve with redshift.The photoionization rate Γ is expected to depend on redshift,as the ionizing photons come from the evolving populations of starforming galaxies and quasars.We perform further tests on the T0-γ constraints by modeling fJ(z) and Γ(z).

    Gnedin &Hui(1998)derive an analytic expression of λFin linear theory,

    To test the potential effect of the evolution of fJ(z)=λF(z)/λJ(z) on our constraints, we compute fJ(z) by adopting an IGM temperature evolution similar in shape to that in Villasenor et al.(2022), starting from T0~0K at z ?7 and increasing to T0?104K at lower redshifts with two bumps at z ~6 and z ~3 caused by H I and He II reionization,respectively.The values of fJare scaled such that fJ(z=3)=0.88 to match the fiducial value tuned in Garzilli et al.(2015).The resultant fJ(z) is ~0.9 for 2.9 <z <3.6 and ramps up toward lower redshifts to a value of ~1.27 at z ~1.6.

    In the redshift range of interest here, the empirically measured hydrogen photoionization rate Γ only shows a mild evolution (e.g., Becker et al.2007, 2013;Villasenor et al.2022).We model the evolution to be Γ(z)=10-12s-1[(1+z)/2.6]-1, consistent with the model in Haardt & Madau (2012) and those empirical measurements with a steeper evolution.

    Figure 4.Similar to Figure 3,but our constraints are compared to those with evolving model parameters.The red and blue open circles are the same as in Figure 3,where fJ and Γ parameters in the analytic model are fixed at their fiducial values.The pink and cyan filled circles are constraints when allowing fJ and Γ to evolve with redshift.See the text for details.For clarity,the pink and cyan points are shifted by Δz=0.05.The ratios of the latter constraints to the former ones are shown in the small panels, with the shaded regions representing the 1σ uncertainties.

    The test results with the evolving fJand Γ are shown in Figure 4, in comparison with the fiducial results.For the constraints using the 10th percentile b cutoff estimated nonparametrically (top panels), T0appears to be slightly lower at lower redshifts, before reaching the peak.The value of γ is slightly higher at lower redshifts and lower at higher redshifts.Each lower small panel shows the ratio of the constraints to those from the fiducial ones, and all the changes in the constraints caused by the evolving fJand Γ are well within the 1σ uncertainty.

    For the results using the b cutoff determined by a parametric fit to the b distribution(bottom panels),the trends are similar to those in the top panels, but with changes of larger amplitude.For γ, the changes are still well within the 1σ uncertainty.For T0,most of the changes are also within 1σ and others are within 1.5σ(if accounting for uncertainties in the constraints with both fixed and varying fJand Γ).For both methods, adopting the evolving fJand Γ leads to constraints more in line with those from Gaikwad et al.(2021) and Villasenor et al.(2022) at lower redshifts.

    As a whole, the tests demonstrate that fixing the parameters in the analytic model to their fiducial values does not introduce significant systematic trends in the T0-γ constraints with the data we use.The amplitude and shape of the column-densitydependent b cutoff profile of Lyα absorbers atlogNHI∈ [13,15] enable robust constraints on the temperature-density relation of the IGM around z ~3 within the framework of the analytic model.

    4.Summary and Discussion

    Based on the distribution of the neutral hydrogen column density NHIand Doppler b parameter measurements of 1.6 <z <3.6 Lyα absorbers in the Lyα forest regions of high-resolution and high-S/N quasar spectra, we employ an analytic model to constrain T0and γ, the two parameters describing the temperature-density relation of the IGM,T=T0Δγ-1.The constraints come from the NHI-dependent low b cutoff, contributed by Lyα absorbers dominated by thermal broadening.The IGM temperature T0at the mean density shows a peak of ~1.5×104K at z ~2.7–2.9 and drops to ~104K at the lower and higher end of the redshift range.The index γ reaches a minimum around z ~3.The evolution in both parameters signals that He II reionization finishes around z ~3.

    The low b cutoff profile as a function of NHIis obtained using two methods.The first one is a non-parametric method.With the measured values of NHIand b and their uncertainties,in each NHIbin,we compute the cumulative distribution of the measured b parameter to find the cutoff value corresponding to the lower 10th percentile and the uncertainty in the cutoff value is obtained through bootstrapping.The second method is a parametric one.In each NHIbin, we fit the b distribution with an analytic function (Hui & Rutledge 1999) using a maximum likelihood method to infer the 10th-percentile b cutoff value.The analytic model developed in Garzilli et al.(2015) is then applied to model these b cutoff profiles to obtain the T0-γ constraints.For T0, using the b cutoff profiles estimated from the two methods leads to similar constraints.For γ,using the b cutoff profile from fitting the b distribution results in lower values of γ than that using the non-parametrically inferred b cutoff.This may result from the fact that the analytic model is effectively calibrated with the first method.Nevertheless, the constraints of γ with b cutoff profiles from the two methods are consistent within 2σ in most redshift bins.In obtaining the constraints,we use NHIand b parameters measured from fitting the Lyman series lines and from only fitting the Lyα lines,respectively, and the results agree with each other.

    Our results are in line with some recent T0–γ constraints from completely different approaches.Those include Gaikwad et al.(2021),who measure the IGM thermal state by using four different flux statistics in the Lyα forest regions of highresolution and high-S/N quasar spectra and by using a code developed to efficiently construct models with a wide range of IGM thermal and ionization histories without running full hydrodynamic simulations.Our results also agree with those in Villasenor et al.(2022), where the constraints on the IGM thermal and ionization history are obtained from modeling the one-dimensional Lyα forest power spectrum with a massive suite of more than 400 high-resolution cosmological hydrodynamic simulations.These nontrivial agreements with other work of different approaches suggest that the analytic model we adopt not only correctly captures the main physics in the low b cutoff but also is reasonably calibrated.

    There are a few model parameters in the analytic model: fJrelates the Jeans length to the filtering (smoothing) scale, fNis the proportional coefficient in determining the neutral hydrogen column density from the neutral hydrogen number density and the filtering scale, and Γ is the hydrogen photoionization rate.At high NHIthat we mainly use for the T0–γ constraints, the b cutoff profiles and hence the constraints are insensitive to these parameters, e.g., with b2approximately depending on(fJ fNΓ)-0.25.We further test the sensitivity by adopting an evolving fJfactor from linear theory and an assumed thermal evolution of the IGM and an observationally and theoretically motivated Γ evolution, and we find no significant changes in the constraints.That is, adopting the fiducial values of the model parameters result in no significant systematic trend in the T0–γ constraints within the framework of the analytic model and with the observational data in our analysis.

    The analytic model, with its current functional form, however,could still have systematic uncertainties in that it may not perfectly fit the results from the hydrodynamic simulations.Garzilli et al.(2020) have discussed the possible improvements to the model.While directly using simulations to perform parameter constraints(e.g.,Villasenor et al.2022)is a route to largely reduce systematic uncertainties,it would still be useful to calibrate an analytic model with a set of hydrodynamic simulations at different output redshifts.To be self-consistent,model parameters like fJand Γ should encode the dependence on the IGM’s thermal and ionization history.The model can also be calibrated to accommodate different ways of inferring the b cutoff profile, as well as different percentile thresholds for defining the cutoff(e.g.,Garzilli et al.2020).Such a model would have the advantage of being computationally efficient and can be easily applied to model observed Lyα absorbers to learn about the physical properties of the IGM.

    At z ?3, when He II reionization is not complete, a large number of sightlines are needed to fully probe the IGM state with patchy He II reionization.The sample of the 24 highresolution and high-S/N quasar spectra used in our analysis may still have appreciable cosmic variance (more exactly sample variance) effects, and the uncertainties in our T0and γ may have been underestimated.In fact, this is true for the constraints in most work.A large sample of Lyα forest absorbers from high-resolution and high-S/N quasar spectra is desired to probe the IGM state and He II reionization, which would help tighten the constraints on T0and γ and also make it possible to constrain quantities like fJand Γ.

    Acknowledgments

    This work is supported by the National Key R&D Program of China (Grant No.2018YFA0404503).L.Y.gratefully acknowledges the support of China Scholarship Council (No.201804910563)and the hospitality of the Department of Physics and Astronomy at the University of Utah during her visit.Z.Z.is supported by NSF grant AST-2007499.The support and resources from the Center for High Performance Computing at the University of Utah are gratefully acknowledged.

    Appendix

    In Figure A1, we show the constraints in the T0–γ plane for different redshift bins, using b cutoff profile estimated non-parametrically from the data (top panels) and parametrically from fitting the b distribution,with absorber NHIand b measurements based on the Lyman series fit (left panels)and the Lyα-only fit (right panels).As discussed in Section 3.4, with the relation between the b cutoff and NHI, the constraints on T0are mainly from the relation’s amplitude, while those on γ come from its shape.At each redshift, the constraints in the T0–γ show a degeneracy direction: a higher T0is compensated by a lower γ.This is easy to understand—with a higher T0(hence higher amplitude from the model), a lower γ value can tilt the model so that the amplitude of the b cutoff profile toward high NHIcan be lowered.

    Figure A1.Joint constraints on the IGM temperature-density relation parameters,T0 and γ,from NH I and b values measured based on the Lyman series fit(left panels)and Lyα-only fit(right panels).The constraints in the top panels are derived using the b cutoff relation estimated from the data,while those in the bottom panels are from the b cutoff relation inferred from fitting the b distribution.The contours show the central 39% of the distribution for the two parameters.

    Table A1 Constraints on T0 and γ at Different Redshifts, Using NH I-dependent b Cutoff Profile Estimated Non-parametrically from the Cumulative b Distribution (“10th Percentiles”)and Parametrically from Fitting the Full b Distribution(“ σb ln 10 14( ) ”),with Absorber NH I and b Measurements Based on the Lyman Series Fit and the Lyα-only Fit

    ORCID iDs

    Li Yang https://orcid.org/0000-0001-5353-2957

    午夜福利在线观看吧| 捣出白浆h1v1| 1024香蕉在线观看| 亚洲av片天天在线观看| 麻豆成人av在线观看| 久热爱精品视频在线9| 亚洲五月色婷婷综合| 国产精品久久久久久精品电影小说| 黄色 视频免费看| 国产一区二区三区视频了| 午夜激情av网站| 亚洲欧美激情在线| av天堂在线播放| av线在线观看网站| 精品国产超薄肉色丝袜足j| 少妇粗大呻吟视频| 91麻豆精品激情在线观看国产 | 黄色片一级片一级黄色片| 人人妻人人澡人人看| 最新在线观看一区二区三区| 在线av久久热| 中文字幕高清在线视频| 久久精品亚洲熟妇少妇任你| 又紧又爽又黄一区二区| 国产一区二区三区视频了| 国产免费av片在线观看野外av| 欧美黑人欧美精品刺激| 色94色欧美一区二区| 99国产综合亚洲精品| 久久久国产成人免费| 色婷婷av一区二区三区视频| 欧美另类亚洲清纯唯美| 国产亚洲精品一区二区www | 精品国产超薄肉色丝袜足j| 亚洲国产成人一精品久久久| 80岁老熟妇乱子伦牲交| 国产精品九九99| 久久人妻福利社区极品人妻图片| 免费在线观看黄色视频的| 欧美黄色淫秽网站| 亚洲精品国产色婷婷电影| 亚洲精品国产色婷婷电影| 日日摸夜夜添夜夜添小说| 欧美人与性动交α欧美软件| 亚洲va日本ⅴa欧美va伊人久久| 国产精品影院久久| avwww免费| 91麻豆精品激情在线观看国产 | 黑人巨大精品欧美一区二区蜜桃| 搡老岳熟女国产| 久久久欧美国产精品| 大型av网站在线播放| 国产精品偷伦视频观看了| 日本一区二区免费在线视频| xxxhd国产人妻xxx| 一本久久精品| 热re99久久精品国产66热6| 午夜福利乱码中文字幕| 国产一区二区三区综合在线观看| 成人18禁高潮啪啪吃奶动态图| 久久午夜综合久久蜜桃| 丝袜美足系列| 好男人电影高清在线观看| 啦啦啦免费观看视频1| 18禁国产床啪视频网站| 精品一品国产午夜福利视频| 肉色欧美久久久久久久蜜桃| 91国产中文字幕| aaaaa片日本免费| 国产精品亚洲av一区麻豆| 最近最新中文字幕大全电影3 | 国产男靠女视频免费网站| 宅男免费午夜| 少妇裸体淫交视频免费看高清 | 热re99久久国产66热| 无限看片的www在线观看| 亚洲专区中文字幕在线| 飞空精品影院首页| 麻豆成人av在线观看| 精品一区二区三区av网在线观看 | 黄频高清免费视频| 日韩欧美一区视频在线观看| 国产深夜福利视频在线观看| 亚洲欧美激情在线| 九色亚洲精品在线播放| av电影中文网址| 亚洲av成人一区二区三| 久久青草综合色| svipshipincom国产片| 亚洲色图综合在线观看| 中文字幕精品免费在线观看视频| 久久婷婷成人综合色麻豆| 色在线成人网| 国产伦人伦偷精品视频| 1024视频免费在线观看| 亚洲伊人久久精品综合| 咕卡用的链子| 另类精品久久| 精品一区二区三卡| 国产成人精品无人区| 女警被强在线播放| 一级毛片电影观看| 日韩一区二区三区影片| tube8黄色片| 欧美黑人欧美精品刺激| 最黄视频免费看| 多毛熟女@视频| 国产精品亚洲av一区麻豆| 无限看片的www在线观看| 999精品在线视频| av在线播放免费不卡| 老鸭窝网址在线观看| 日本wwww免费看| 国产片内射在线| 亚洲五月色婷婷综合| 精品亚洲成国产av| 国产在线视频一区二区| 午夜精品久久久久久毛片777| 自拍欧美九色日韩亚洲蝌蚪91| 女人精品久久久久毛片| 啦啦啦中文免费视频观看日本| 女性被躁到高潮视频| 欧美日韩黄片免| 久久久久精品人妻al黑| 99re6热这里在线精品视频| 亚洲国产看品久久| 乱人伦中国视频| 亚洲精品在线观看二区| 一级a爱视频在线免费观看| 欧美精品亚洲一区二区| 午夜福利视频在线观看免费| 亚洲国产毛片av蜜桃av| 亚洲成人免费av在线播放| 丁香欧美五月| 国产淫语在线视频| 在线观看人妻少妇| 动漫黄色视频在线观看| 一本综合久久免费| 91九色精品人成在线观看| 久热爱精品视频在线9| 97人妻天天添夜夜摸| 欧美精品啪啪一区二区三区| 亚洲一区中文字幕在线| 色播在线永久视频| 精品人妻在线不人妻| 国产在线一区二区三区精| 不卡av一区二区三区| 两个人看的免费小视频| 男男h啪啪无遮挡| av网站在线播放免费| e午夜精品久久久久久久| 亚洲第一欧美日韩一区二区三区 | 夫妻午夜视频| 亚洲va日本ⅴa欧美va伊人久久| 午夜视频精品福利| 日韩欧美一区二区三区在线观看 | 久久九九热精品免费| 又大又爽又粗| 一级,二级,三级黄色视频| 免费观看av网站的网址| 菩萨蛮人人尽说江南好唐韦庄| 日韩免费高清中文字幕av| 亚洲国产欧美日韩在线播放| 男女无遮挡免费网站观看| av超薄肉色丝袜交足视频| 最新在线观看一区二区三区| 王馨瑶露胸无遮挡在线观看| 久久狼人影院| 中文字幕另类日韩欧美亚洲嫩草| 日本一区二区免费在线视频| 五月天丁香电影| 91成人精品电影| kizo精华| 久久这里只有精品19| 亚洲 欧美一区二区三区| 久热爱精品视频在线9| 超碰成人久久| 啦啦啦免费观看视频1| 国内毛片毛片毛片毛片毛片| 亚洲欧洲日产国产| 五月天丁香电影| 免费黄频网站在线观看国产| 51午夜福利影视在线观看| 国产黄色免费在线视频| 久久中文字幕一级| 精品乱码久久久久久99久播| 黑丝袜美女国产一区| 91成年电影在线观看| 亚洲中文av在线| 黑丝袜美女国产一区| 精品视频人人做人人爽| 黄色视频不卡| 国产精品.久久久| 国产亚洲精品久久久久5区| 欧美成狂野欧美在线观看| 午夜老司机福利片| 亚洲人成电影观看| 国产av又大| 精品一区二区三区四区五区乱码| 久久ye,这里只有精品| 青青草视频在线视频观看| 99久久99久久久精品蜜桃| 久久久久久免费高清国产稀缺| 欧美 日韩 精品 国产| 好男人电影高清在线观看| 18禁国产床啪视频网站| 久久久久精品人妻al黑| 天天添夜夜摸| 免费观看av网站的网址| 日本撒尿小便嘘嘘汇集6| 精品久久蜜臀av无| 午夜成年电影在线免费观看| 黑人欧美特级aaaaaa片| 丝袜美足系列| 免费日韩欧美在线观看| 91字幕亚洲| 在线观看一区二区三区激情| 午夜福利一区二区在线看| 精品人妻熟女毛片av久久网站| 国产亚洲欧美在线一区二区| 免费女性裸体啪啪无遮挡网站| 一级片免费观看大全| 麻豆av在线久日| 热99re8久久精品国产| 欧美国产精品va在线观看不卡| 亚洲少妇的诱惑av| 午夜福利免费观看在线| 多毛熟女@视频| 九色亚洲精品在线播放| 免费少妇av软件| 欧美日韩成人在线一区二区| 国产精品一区二区免费欧美| 久久久久网色| 日本黄色日本黄色录像| 成年人黄色毛片网站| √禁漫天堂资源中文www| 亚洲精品中文字幕在线视频| 欧美黑人欧美精品刺激| 亚洲精品乱久久久久久| 亚洲专区字幕在线| 嫩草影视91久久| 中亚洲国语对白在线视频| 久久久久国产一级毛片高清牌| 国产日韩一区二区三区精品不卡| 国产精品久久电影中文字幕 | 亚洲av第一区精品v没综合| 丝袜人妻中文字幕| 一进一出抽搐动态| 99热国产这里只有精品6| 最新在线观看一区二区三区| 国产激情久久老熟女| 欧美久久黑人一区二区| 丰满少妇做爰视频| 亚洲精品在线观看二区| 午夜福利视频在线观看免费| 亚洲视频免费观看视频| 老汉色av国产亚洲站长工具| 99国产综合亚洲精品| 精品国产乱码久久久久久小说| 美女主播在线视频| 首页视频小说图片口味搜索| 黑人猛操日本美女一级片| 欧美精品av麻豆av| 久久久久久久久免费视频了| 亚洲专区字幕在线| a级毛片黄视频| 丰满饥渴人妻一区二区三| 少妇 在线观看| 亚洲伊人色综图| 午夜免费鲁丝| 大型黄色视频在线免费观看| 叶爱在线成人免费视频播放| 黄色a级毛片大全视频| 久久精品国产a三级三级三级| 大香蕉久久网| 18在线观看网站| 国产在视频线精品| 日本欧美视频一区| 日韩人妻精品一区2区三区| 亚洲午夜理论影院| 天天躁狠狠躁夜夜躁狠狠躁| 电影成人av| 免费看十八禁软件| 高清欧美精品videossex| 丁香欧美五月| 天堂中文最新版在线下载| 午夜免费鲁丝| 免费黄频网站在线观看国产| 精品熟女少妇八av免费久了| 国产亚洲精品一区二区www | 国产精品久久久久久精品古装| 一夜夜www| 亚洲人成电影免费在线| 久久久精品国产亚洲av高清涩受| 久久久国产欧美日韩av| 精品人妻在线不人妻| 露出奶头的视频| av网站免费在线观看视频| 日韩有码中文字幕| www.精华液| 精品高清国产在线一区| 一本综合久久免费| 精品国产国语对白av| 亚洲成人免费av在线播放| 亚洲成人国产一区在线观看| 欧美日韩中文字幕国产精品一区二区三区 | 极品少妇高潮喷水抽搐| 免费高清在线观看日韩| 国产精品久久电影中文字幕 | 18禁国产床啪视频网站| 国产免费福利视频在线观看| 波多野结衣一区麻豆| 精品欧美一区二区三区在线| 久久国产精品人妻蜜桃| 精品国产国语对白av| 麻豆成人av在线观看| 18禁观看日本| 午夜福利乱码中文字幕| 久久久国产精品麻豆| 又大又爽又粗| 女人精品久久久久毛片| 精品国产乱子伦一区二区三区| 亚洲欧美一区二区三区久久| 欧美成人午夜精品| 午夜精品国产一区二区电影| 日韩熟女老妇一区二区性免费视频| 亚洲av国产av综合av卡| 久久青草综合色| 国产日韩欧美亚洲二区| 国产在线免费精品| 久久国产精品人妻蜜桃| 十八禁高潮呻吟视频| 波多野结衣一区麻豆| 高清欧美精品videossex| 久久国产精品男人的天堂亚洲| 一进一出抽搐动态| 激情在线观看视频在线高清 | 亚洲七黄色美女视频| 久久久精品94久久精品| 中文字幕制服av| 中文欧美无线码| 9191精品国产免费久久| 久久久水蜜桃国产精品网| 国产97色在线日韩免费| 免费在线观看影片大全网站| 欧美av亚洲av综合av国产av| 99riav亚洲国产免费| 久久青草综合色| 日韩欧美三级三区| 菩萨蛮人人尽说江南好唐韦庄| 美女视频免费永久观看网站| 纵有疾风起免费观看全集完整版| 久久久久久久久免费视频了| 欧美午夜高清在线| av福利片在线| 亚洲精品av麻豆狂野| 国产在线观看jvid| 精品熟女少妇八av免费久了| 婷婷成人精品国产| 香蕉丝袜av| 精品欧美一区二区三区在线| 丝袜喷水一区| 国产黄频视频在线观看| 国产高清videossex| 国产精品久久久久久精品古装| 国产主播在线观看一区二区| 性色av乱码一区二区三区2| 首页视频小说图片口味搜索| 丰满少妇做爰视频| 免费黄频网站在线观看国产| 天天躁狠狠躁夜夜躁狠狠躁| 叶爱在线成人免费视频播放| 99热网站在线观看| 久久精品亚洲精品国产色婷小说| 久久久久久久国产电影| 精品免费久久久久久久清纯 | 在线观看免费视频网站a站| 国产男女超爽视频在线观看| 国产精品亚洲av一区麻豆| 国产亚洲精品一区二区www | 午夜久久久在线观看| 欧美日本中文国产一区发布| av网站在线播放免费| 国产又爽黄色视频| 国产极品粉嫩免费观看在线| 亚洲中文字幕日韩| 日本a在线网址| 欧美国产精品一级二级三级| 亚洲精品中文字幕在线视频| 国产免费福利视频在线观看| 亚洲国产欧美网| 亚洲视频免费观看视频| 国产成人免费观看mmmm| 欧美精品啪啪一区二区三区| 久久亚洲真实| 精品少妇内射三级| 久久中文字幕一级| 久久青草综合色| 久久久水蜜桃国产精品网| 三级毛片av免费| 午夜激情av网站| 男女边摸边吃奶| 在线观看舔阴道视频| 久久精品熟女亚洲av麻豆精品| 两性夫妻黄色片| 曰老女人黄片| 精品国产一区二区三区久久久樱花| 大片免费播放器 马上看| 80岁老熟妇乱子伦牲交| 国产精品欧美亚洲77777| 97在线人人人人妻| 这个男人来自地球电影免费观看| 亚洲精品在线美女| 大型av网站在线播放| 亚洲国产欧美网| h视频一区二区三区| 免费不卡黄色视频| 国产成+人综合+亚洲专区| 高清视频免费观看一区二区| 99久久国产精品久久久| 亚洲精品久久午夜乱码| 麻豆成人av在线观看| 午夜福利一区二区在线看| 大型av网站在线播放| 丝袜人妻中文字幕| 黄色丝袜av网址大全| 女性被躁到高潮视频| h视频一区二区三区| 老鸭窝网址在线观看| 国产成人精品久久二区二区免费| 纯流量卡能插随身wifi吗| 成年人免费黄色播放视频| av超薄肉色丝袜交足视频| √禁漫天堂资源中文www| 日韩中文字幕欧美一区二区| 老司机影院毛片| 成人三级做爰电影| 色老头精品视频在线观看| 老汉色av国产亚洲站长工具| 亚洲avbb在线观看| 免费在线观看完整版高清| 午夜激情久久久久久久| 国产不卡av网站在线观看| 国产精品亚洲av一区麻豆| 在线观看一区二区三区激情| 99精品久久久久人妻精品| 一级a爱视频在线免费观看| 18禁美女被吸乳视频| 啦啦啦视频在线资源免费观看| 在线 av 中文字幕| 香蕉丝袜av| 一级毛片精品| 午夜福利在线免费观看网站| 精品人妻在线不人妻| 亚洲精品乱久久久久久| 天天影视国产精品| 一区二区av电影网| 久久精品国产a三级三级三级| 久久久国产成人免费| 国产99久久九九免费精品| 女人久久www免费人成看片| 最近最新中文字幕大全电影3 | 黑人欧美特级aaaaaa片| 久久精品熟女亚洲av麻豆精品| 黄色丝袜av网址大全| 国产又爽黄色视频| 丝袜美腿诱惑在线| 日日爽夜夜爽网站| 久久中文看片网| 窝窝影院91人妻| 亚洲视频免费观看视频| 桃花免费在线播放| 欧美在线黄色| 首页视频小说图片口味搜索| 久久国产精品男人的天堂亚洲| 亚洲成a人片在线一区二区| 久久久久久免费高清国产稀缺| 国产极品粉嫩免费观看在线| 亚洲精品在线美女| 久久久久久久精品吃奶| 香蕉久久夜色| 国产欧美亚洲国产| 91精品国产国语对白视频| 99在线人妻在线中文字幕 | 国产麻豆69| 波多野结衣av一区二区av| av福利片在线| 亚洲少妇的诱惑av| 国产成人一区二区三区免费视频网站| 变态另类成人亚洲欧美熟女 | 在线看a的网站| 午夜日韩欧美国产| 国产欧美日韩一区二区三| 国产精品 欧美亚洲| 亚洲av成人不卡在线观看播放网| 成人国产av品久久久| 国产精品久久久人人做人人爽| 最近最新中文字幕大全电影3 | 丁香六月欧美| 国产在线免费精品| 男女高潮啪啪啪动态图| 在线天堂中文资源库| 最新美女视频免费是黄的| 亚洲av美国av| 欧美精品av麻豆av| 悠悠久久av| 日韩大片免费观看网站| 纯流量卡能插随身wifi吗| 国产精品亚洲av一区麻豆| 精品人妻1区二区| 亚洲人成伊人成综合网2020| 成人特级黄色片久久久久久久 | 90打野战视频偷拍视频| 免费一级毛片在线播放高清视频 | 亚洲黑人精品在线| 午夜福利视频精品| 高清黄色对白视频在线免费看| 又黄又粗又硬又大视频| 最新的欧美精品一区二区| bbb黄色大片| 男女午夜视频在线观看| 操美女的视频在线观看| 亚洲国产欧美日韩在线播放| 国产单亲对白刺激| 色在线成人网| 久久久久精品国产欧美久久久| 另类亚洲欧美激情| 欧美日韩亚洲国产一区二区在线观看 | 亚洲精品乱久久久久久| 纯流量卡能插随身wifi吗| 精品欧美一区二区三区在线| 国产精品麻豆人妻色哟哟久久| 国产高清国产精品国产三级| 一区福利在线观看| 一本—道久久a久久精品蜜桃钙片| 两个人免费观看高清视频| 亚洲精品国产一区二区精华液| 美女高潮喷水抽搐中文字幕| 人人妻人人添人人爽欧美一区卜| 两个人免费观看高清视频| 黄色毛片三级朝国网站| 精品乱码久久久久久99久播| 亚洲avbb在线观看| 国产精品香港三级国产av潘金莲| 精品久久久久久电影网| 一区福利在线观看| 国产男女内射视频| 搡老岳熟女国产| 成人手机av| 日本黄色视频三级网站网址 | 啦啦啦视频在线资源免费观看| 美女高潮到喷水免费观看| 丁香六月欧美| 国产一区二区三区在线臀色熟女 | 久久中文看片网| 精品卡一卡二卡四卡免费| 露出奶头的视频| 我的亚洲天堂| 乱人伦中国视频| 极品人妻少妇av视频| 五月天丁香电影| 1024香蕉在线观看| 久久性视频一级片| 麻豆乱淫一区二区| 久久久久精品人妻al黑| 岛国在线观看网站| 香蕉丝袜av| 9热在线视频观看99| 久久久久国内视频| 1024视频免费在线观看| 水蜜桃什么品种好| 一夜夜www| 黄色成人免费大全| 成年人黄色毛片网站| 999久久久国产精品视频| 国产成人欧美在线观看 | 日韩免费高清中文字幕av| 国产成人精品久久二区二区91| 一边摸一边做爽爽视频免费| 99久久国产精品久久久| 天天影视国产精品| 少妇的丰满在线观看| 国产真人三级小视频在线观看| 亚洲avbb在线观看| 久久av网站| 精品高清国产在线一区| 久久中文字幕人妻熟女| 王馨瑶露胸无遮挡在线观看| 美女午夜性视频免费| 大片电影免费在线观看免费| 亚洲欧美日韩另类电影网站| 久久国产精品大桥未久av| 亚洲第一欧美日韩一区二区三区 | 亚洲成人免费电影在线观看| 两性夫妻黄色片| 9热在线视频观看99| 日韩欧美三级三区| 国产精品电影一区二区三区 | 咕卡用的链子| 精品少妇黑人巨大在线播放| 欧美中文综合在线视频| 蜜桃在线观看..| av又黄又爽大尺度在线免费看| 动漫黄色视频在线观看| 99香蕉大伊视频| 在线观看www视频免费| 亚洲,欧美精品.| 亚洲成国产人片在线观看| 欧美+亚洲+日韩+国产| 精品久久久久久久毛片微露脸| 日日爽夜夜爽网站| 亚洲成人免费av在线播放| 国产在线精品亚洲第一网站| 十八禁网站网址无遮挡| 色老头精品视频在线观看|