Z-transformed Discrete Correlation Function Research Articles

Continuum reverberation mapping of MCG 08-11-011

Aims. We report the results from a photometric reverberation mapping campaign carried out with the C18 telescope at the Wise Observatory from 2019 to 2020, targeting the active galactic nucleus (AGN) MCG 08-11-011. The monitoring was conducted on a daily basis with specially designed narrow-band filters, spanning from optical to near-infrared wavelengths (∼4000 to 8000 Å) and avoiding prominent broad emission lines. We aim to measure inter-band continuum time lags, determine the size–wavelength relation, and estimate the host-subtracted AGN luminosity for this system. Methods. We used the point-spread function photometry to extract the continuum light curves and measure the inter-band time lags using several methods, including the interpolated cross-correlation function, the z-transformed discrete correlation function, a von Neumann estimator, JAVELIN (in spectroscopic and photometric mode), MICA, and a multivariate correlation function. Results. We find wavelength-dependent lags, τ(λ), up to ∼7 days between the multiband light curves of MCG 08-11-011. The observed lags are larger than predictions based on standard thin-disk theory by a factor of ∼3 − 7. We discern a significantly steeper (τ ∝ λ4.74) size-wavelength relation than the τ ∝ λ4/3 expected for a geometrically thin and optically thick accretion disk, which may result from the contribution of diffuse continuum emission to the flux. These results are similar to those found by previous continuum reverberation mapping campaigns.

Long-term multi-wavelength study of 1ES 0647+250

Context. The BL Lac object 1ES 0647+250 is one of the few distant γ-ray emitting blazars detected at very high energies (VHEs; ≳100 GeV) during a non-flaring state. It was detected with the MAGIC telescopes during a period of low activity in the years 2009−2011 as well as during three flaring activities in the years 2014, 2019, and 2020, with the highest VHE flux in the last epoch. An extensive multi-instrument data set was collected as part of several coordinated observing campaigns over these years. Aims. We aim to characterise the long-term multi-band flux variability of 1ES 0647+250, as well as its broadband spectral energy distribution (SED) during four distinct activity states selected in four different epochs, in order to constrain the physical parameters of the blazar emission region under certain assumptions. Methods. We evaluated the variability and correlation of the emission in the different energy bands with the fractional variability and the Z-transformed discrete correlation function, as well as its spectral evolution in X-rays and γ rays. Owing to the controversy in the redshift measurements of 1ES 0647+250 reported in the literature, we also estimated its distance in an indirect manner through a comparison of the GeV and TeV spectra from simultaneous observations with Fermi-LAT and MAGIC during the strongest flaring activity detected to date. Moreover, we interpret the SEDs from the four distinct activity states within the framework of one-component and two-component leptonic models, proposing specific scenarios that are able to reproduce the available multi-instrument data. Results. We find significant long-term variability, especially in X-rays and VHE γ rays. Furthermore, significant (3−4σ) correlations were found between the radio, optical, and high-energy (HE) γ-ray fluxes, with the radio emission delayed by about ∼400 days with respect to the optical and γ-ray bands. The spectral analysis reveals a harder-when-brighter trend during the non-flaring state in the X-ray domain. However, no clear patterns were observed for either the enhanced states or the HE (30 MeV < E < 100 GeV) and VHE γ-ray emission of the source. The indirect estimation of the redshift yielded a value of z = 0.45 ± 0.05, which is compatible with some of the values reported in the literature. The SEDs related to the low-activity state and the three flaring states of 1ES 0647+250 can be described reasonably well with the both one-component and two-component leptonic scenarios. However, the long-term correlations indicate the need for an additional radio-producing region located about 3.6 pc downstream from the gamma-ray producing region.

Continuum reverberation mapping of the quasar PG 2130+099

Aims. We present the results of an intensive six-month optical continuum reverberation mapping campaign of the Seyfert 1 galaxy PG 2130+099 at redshift z = 0.063. The ground-based photometric monitoring was conducted on a daily basis with the robotic 46 cm telescope of the WISE observatory located in Israel. Specially designed narrowband filters were used to observe the central engine of the active galactic nucleus (AGN), avoiding line contamination from the broad-line region (BLR). We aim to measure inter-band continuum time lags across the optical range and determine the size-wavelength relation for this system. Methods. We used two methods, the traditional point-spread function photometry and the recently developed proper image subtraction technique, to independently perform the extraction of the continuum light curves. The inter-band time lags are measured with several methods, including the interpolated cross-correlation function, the z-transformed discrete correlation function, a von Neumann estimator, JAVELIN (in spectroscopic mode), and MICA. Results. PG 2130+099 displays correlated variability across the optical range, and we successfully detect significant time lags of up to ∼3 days between the multiband light curves. We find that the wavelength-dependent lags, τ(λ), generally follow the relation τ(λ)∝λ4/3, as expected for the temperature radial profile T ∝ R−3/4 of an optically thick, geometrically thin accretion disk. Despite that, the derived time lags can also be fitted by τ(λ)∝λ2, implying the possibility of a slim, rather than thin, accretion disk. Using the flux variation gradient method, we determined the AGN’s host-galaxy-subtracted rest frame 5100 Å luminosity at the time of our monitoring campaign with an uncertainty of ∼18% (λL5100 = (2.40 ± 0.42)×1044 erg s−1). While a continuum reprocessing model can fit the data reasonably well, our derived disk sizes are a factor of ∼2 − 6 larger than the theoretical disk sizes predicted from the AGN luminosity estimate of PG 2130+099. This result is in agreement with previous studies of AGN/quasars and suggests that the standard Shakura-Sunyaev disk theory has limitations in describing AGN accretion disks.

Time-delay Measurement of Mg ii Broad-line Response for the Highly Accreting Quasar HE 0413-4031: Implications for the Mg ii–based Radius–Luminosity Relation

Abstract We present the monitoring of the active galactic nuclei continuum and Mg ii broad-line emission for the quasar HE 0413-4031 (z = 1.38) based on the six-year monitoring by the South African Large Telescope (SALT). We manage to estimate a time-delay of days in the rest frame of the source using seven different methods: interpolated cross-correlation function, discrete correlation function (DCF), z-transformed DCF, JAVELIN, two estimators of data regularity (Von Neumann, Bartels), and χ 2 method. This time-delay is below the value expected from the standard radius–luminosity relation. However, based on the monochromatic luminosity of the source and the spectral energy distribution modeling, we interpret this departure as the shortening of the time-delay due to the higher accretion rate of the source, with the inferred Eddington ratio of ∼0.4. The Mg ii line luminosity of HE 0413-4031 responds to the continuum variability as , which is consistent with the light-travel distance of the location of Mg ii emission at R out ∼ 1018 cm. Using the data of 10 other quasars, we confirm the radius–luminosity relation for the broad Mg ii line, which was previously determined for the broad Hβ line for lower-redshift sources. In addition, we detect a general departure of higher-accreting quasars from this relation in analogy to the Hβ sample. After the accretion-rate correction of the light-travel distance, the Mg ii–based radius–luminosity relation has a small scatter of only 0.10 dex.

The Sloan Digital Sky Survey Reverberation Mapping Project: Comparison of Lag Measurement Methods with Simulated Observations

Abstract We investigate the performance of different methodologies that measure the time lag between broad-line and continuum variations in reverberation mapping data using simulated light curves that probe a range of cadence, time baseline, and signal-to-noise ratio in the flux measurements. We compare three widely adopted lag-measuring methods: the interpolated cross-correlation function (ICCF), the z-transformed discrete correlation function (ZDCF), and the Markov chain Monte Carlo code JAVELIN, for mock data with qualities typical of multiobject spectroscopic reverberation mapping (MOS-RM) surveys that simultaneously monitor hundreds of quasars. We quantify the overall lag-detection efficiency, the rate of false detections, and the quality of lag measurements for each of these methods and under different survey designs (e.g., observing cadence and depth) using mock quasar light curves. Overall JAVELIN and ICCF outperform ZDCF in essentially all tests performed. Compared with ICCF, JAVELIN produces higher quality lag measurements, is capable of measuring more lags with timescales shorter than the observing cadence, is less susceptible to seasonal gaps and signal-to-noise ratio degradation in the light curves, and produces more accurate lag uncertainties. We measure the Hβ broad-line region size–luminosity (R–L) relation with each method using the simulated light curves to assess the impact of selection effects of the design of MOS-RM surveys. The slope of the R–L relation measured by JAVELIN is the least biased among the three methods and is consistent across different survey designs. These results demonstrate a clear preference for JAVELIN over the other two nonparametric methods for MOS-RM programs, particularly in the regime of limited light-curve quality as expected from most MOS-RM programs.

Search for Intra-day Optical Variability in γ-Ray-loud Blazars S5 0716+714 and 3C 273

Abstract We present the photometric observations of blazars S5 0716+714 and 3C 273 with high temporal resolution (30–60 s) in the I or R bands. The observations were performed with a 1.02 m optical telescope from 2007 March 7 to 2012 May 16. The F-test, one-way analysis of variance (ANOVA) test, and z-transformed discrete correlation function (ZDCF) cross-correlation zero lag test are used to search for intra-day variability (IDV). Four and five reliable IDVs survive three tests for S5 0716+714 and 3C 273, respectively. IDVs are found for S5 0716+714 and 3C 273. A flare on 2008 May 8 has ΔI ≈ 0.06 ± 0.01 mag in a duration of 0.54 hr for S5 0716+714. A flare on 2011 May 10 shows ΔR ≈ 0.05 ± 0.01 mag in a duration of 0.40 hr for 3C 273. Sharp dips appear on 2011 May 9 for 3C 273 and show ΔR ≈ 0.05 ± 0.01 mag. Under the assumptions that the IDV is tightly connected to black hole mass, M •, and that the flare durations are representative of the minimum characteristic timescales, we can estimate upper bounds to M •. In the case of the Kerr black holes, M • ≲ 108.91 M ⊙ and M • ≲ 109.02 M ⊙ are given for S5 0716+714 and 3C 273, respectively. These mass measurements are consistent with those measurements reported in the literature. Also, we discuss the origins of optical variations found in this work.

Reverberation mapping of distant quasars: Time lag determination using different methods

AbstractBy applying different statistically robust methods, we analyze the time lag between the continuum and ionized line‐emission (Mg II line) light curves for the distant bright quasar CTS C30.10 (redshift z∼0.9). The data were obtained by the 10‐meter South African Large Telescope (SALT) telescope in South Africa. In detail, we demonstrate the application of several methods using the interpolated cross‐correlation function (ICCF), discrete correlation function (DCF), z‐transformed discrete correlation function (zDCF), von Neumann estimator, and the JAVELIN code package. In particular, we discuss the uncertainties of these methods. In conclusion, we find that the quasar lies on the broad‐line region (BLR) size—monochromatic luminosity power‐law scaling, , which was already confirmed for low‐redshift sources. In case, the BLR size–luminosity relation holds for other distant sources, quasars could be used to probe cosmological models as “standard candles” complementary to supernovae Ia.

Optical multi-color monitoring of the BL Lacertae Object S5 0716+714 with BOOTES-4

S5 0716+714 had been monitored from November, 2017 to May, 2018 with the 60 cm autonomous telescope BOOTES-4 (the fourth station of the BOOTES network), which located at the Lijiang Observatory of the Yunnan Observatories, the Chinese Academy of Sciences. The observations include 125 nights. The time span per night is from 0.026 hours to 10.73 hours (average time span 3.94 hours). The time intervals between two adjacent bands are about 2.23 minutes. With the high quality data, we use one-way analysis of variance (ANOVA) and $F$ -test to check the intraday flux variability (IDV) by considering the 62 nights with time span more than 4 hours. The values of duty cycle (DC) are 77%, 83%, 74% for $g$ , $r$ , $i$ bands respectively. The intraday flux variability amplitude distributions are from 2.54% to 35.35% and the mean value is 16.33%. The analysis of z-transformed discrete correlation function (ZDCF) shows that the significant time lags between different wavebands are not found. The scope of characteristic flux variability timescales is from 0.015 day to 0.164 day, and the mean value is 0.066 day. Most of nights show bluer when brighter (BWB) trends while some nights have weak BWB trends or redder-when brighter (RWB) trends in different brightness. The shock-in-jet model and multiple variation components in the jet could explain the IDV and color behaviors.

Hard X-ray properties of NuSTAR blazars

Context. Investigation of the hard X-ray emission properties of blazars is key to the understanding of the central engine of the sources and associated jet process. In particular, simultaneous spectral and timing analyses of the intraday hard X-ray observations provide us a means to peer into the compact innermost blazar regions that are not accessible to our current instruments. Aims. The primary objective of the work is to associate the observed hard X-ray variability properties in blazars with their flux and spectral states, thereby, based on the correlation among these states, extract the details about the emission regions and processes occurring near the central engine. Methods. We carried out timing, spectral, and cross-correlation analysis of 31 NuSTAR observations of 13 blazars. We investigated the spectral shapes of the sources using single power-law, broken power-law, and log-parabola models. We also studied the co-relation between the soft and hard emission using z-transformed discrete correlation function. In addition, we attempted to constrain the smallest emission regions using minimum variability timescales derived from the light curves. Results. We found that, for most of the sources, the hard X-ray emission can be well represented by the log-parabola model and that the spectral slopes for different blazar subclasses are consistent with the so-called blazar sequence. We also report the steepest spectra (Γ ∼ 3) in the BL Lacertae PKS 2155–304 and the hardest spectra (Γ ∼ 1.4) in the flat-spectrum radio quasar PKS 2149–306. In addition, we noted a close connection between the flux and spectral slope within the source subclass in the sense that high flux and/or flux states tend to be harder in spectra. In BL Lacertae objects, assuming particle acceleration by diffusive shocks and synchrotron cooling as the dominant processes governing the observed flux variability, we constrain the magnetic field of the emission region to be a few Gauss; whereas in flat-spectrum radio quasars, using external Compton models, we estimate the energy of the lower end of the injected electrons to be a few Lorentz factors.

Long-term study of Mkn 421 with the HAGAR Array of Telescopes

Context:The HAGAR Telescope Array at Hanle, Ladakh has been regularly monitoring the nearby blazar Mkn 421 for the past 7yrs. Aims: Blazars show flux variability in all timescales across the electromagnetic spectrum. While there is abundant literature characterizing the short term flares from different blazars, comparatively little work has been done to study the long term variability. We aim to study the long term temporal and spectral variability in the radiation from Mkn 421 during 2009-2015. Methods: We quantify the variability and lognormality from the radio to the VHE bands, and compute the correlations between the various wavebands using the z-transformed discrete correlation function. We construct the Spectral Energy Distribution (SED) contemporaneous with HAGAR observation seasons and fit it with a one zone synchrotron self Compton model to study the spectral variability. Results: The flux is found to be highly variable across all time scales. The variability is energy dependant, and is maximum in the X-ray and Very High Energy (VHE) bands. A strong correlation is found between the Fermi-LAT (gamma) and radio bands, and between Fermi-LAT and optical, but none between Fermi-LAT and X-ray. Lognormality in the flux distribution is clearly detected. This is the third blazar, following BL~Lac and PKS~2155$+$304 to show this behavior. The SED can be well fit by a one zone SSC model, and variations in the flux states can be attributed mainly due to changes in the particle distribution. A strong correlation is seen between the break energy $\gamma_b$ of the particle spectrum and the total bolometric luminosity.

A soft X-ray lag detected in Centaurus A

Abstract We performed time-lag analysis on the X-ray light curves of Centaurus A (Cen A) obtained by the Gas Slit Camera (GSC) aboard the Monitor of All-sky X-ray Image (MAXI) in three energy bands (2–4 keV, 4–10 keV, and 10–20 keV). We discovered a soft X-ray lag relative to higher energies (soft lag) on a timescale of days in a flaring episode by employing the discrete correlation function (DCF) and the z-transformed discrete correlation function (ZDCF) method. In the episode, a peak and a centroid in the DCF and the ZDCF was observed at a soft lag of ∼ 5 d in 2–4 keV versus 4–10 keV and in 4–10 keV versus 10–20 keV, and ∼ 10 d in 2–4 keV versus 10–20 keV. We found it difficult to explain the observed X-ray variation by a single energy injection with the one-zone synchrotron self-Compton (SSC) model, in which the soft lags in these three energy bands reflect the different cooling times of the relativistic electrons, by assuming the magnetic field and minimum Lorentz factor estimated from a broad-band spectral energy distribution. Alternatively, if the phenomenon is interpreted as cooling of Comptonizing electrons in a corona covering the accretion disk, the temperature of the corona producing the variable X-rays should be ∼ 10 keV for reconciliation with the soft lag in the energy range of 2–20 keV.

Underlying particle spectrum of Mkn 421 during the huge X-ray flare in April 2013

Context: In April 2013, the nearby (z=0.031) TeV blazar, Mkn 421, showed one of the largest flares in X-rays since the past decade. Aim: To study all multiwavelength data available during MJD 56392 to 56403, with special emphasis on X-ray data, and understand the underlying particle energy distribution. Methods: We study the correlations between the UV and gamma bands with the X-ray band using the z-transformed discrete correlation function. We model the underlying particle spectrum with a single population of electrons emitting synchrotron radiation, and do a statistical fitting of the simultaneous, time-resolved data from the Swift-XRT and the NuSTAR. Results: There was rapid flux variability in the X-ray band, with a minimum doubling timescale of $1.69 \pm 0.13$ hrs. There were no corresponding flares in UV and gamma bands. The variability in UV and gamma rays are relatively modest with $ \sim 8 \% $ and $\sim 16 \% $ respectively, and no significant correlation was found with the X-ray light curve. The observed X-ray spectrum shows clear curvature which can be fit by a log parabolic spectral form. This is best explained to originate from a log parabolic electron spectrum. However, a broken power law or a power law with an exponentially falling electron distribution cannot be ruled out either. Moreover, the excellent broadband spectrum from $0.3-79$ keV allows us to make predictions of the UV flux. We find that this prediction is compatible with the observed flux during the low state in X-rays. However, during the X-ray flares, the predicted flux is a factor of $2-50$ smaller than the observed one. This suggests that the X-ray flares are plausibly caused by a separate population which does not contribute significantly to the radiation at lower energies. Alternatively, the underlying particle spectrum can be much more complex than the ones explored in this work.

Time series analysis of active galactic nuclei: The case of Arp 102B, 3C 390.3, NGC 5548 and NGC 4051

We used the Z-transformed Discrete Correlation Function (ZDCF) and the Stochastic Process Estimation for AGN Reverberation (SPEAR) methods for the time series analysis of the continuum and the Hα and Hβ line fluxes of a sample of well known type 1 active galactic nuclei (AGNs): Arp 102B, 3C 390.3, NGC 5548, and NGC 4051, where the first two objects are showing double-peaked emission line profiles. The aim of this work is to compare the time lag measurements from these two methods, and check if there is a connection with other emission line properties. We found that the obtained time lags from Hβ are larger than those derived from the Hα analysis for Arp 102B, 3C 390.3 and NGC 5548. This may indicate that the Hβ line originates at larger radii in these objects. Moreover, we found that the ZDCF and SPEAR time lags are highly correlated (r∼0.87), and that the error ranges of both ZDCF and SPEAR time lags are correlated with the FWHM of used emission lines (r∼0.7). This increases the uncertainty of the black hole mass estimates using the virial theorem for AGNs with broader lines.

HINTS OF CORRELATION BETWEEN BROAD-LINE AND RADIO VARIATIONS FOR 3C 120

In the paper, we investigate correlation between broad-line and radio variations for broad-line radio galaxy 3C 120. By the z-transformed discrete correlation function method and the model-independent flux randomization/random subset selection (FR/RSS) Monte Carlo method, we find that the broad Hbeta line variations lead the 15 GHz variations. The FR/RSS method shows that the Hbeta line variations lead the radio variations by a factor of tau_{ob}=0.34 +/- 0.01 yr. This time lag can be used to locate the position of emitting region of radio outbursts in jet, on the order of ~ 5 light-years, from the central engine. This distance is much larger than the size of broad-line region. The large separation of the radio outburst emitting region from the broad-line region will observably influence the gamma-ray emission in 3C 120.

Time Lag in the Intra-Day Variability of Sagittarius A between Light Curves at 90 and 102 GHz

Abstract We performed observations of the flux densities of Sgr A$ ^\star$ at 90 and 102 GHz in order to detect any time lag between these frequencies using the Nobeyama Millimeter Array, which was previously reported at lower frequencies. We detected a radio flare during the observation period on 2005 April 6, and calculated the z-transformed discrete correlation function between the light curves. No time lag between these frequencies was detected. If the expanding plasma model, which explains a time lag at lower frequencies, is valid, the light curve at 90 GHz would be delayed in respect to that at 102 GHz. This result suggests that plasma blobs ejected close to the Galactic center black hole may be widely diverse, especially in optical thickness. Another possibility is that a major portion of the flux above 100 GHz does not originate in blobs.

Time Lag in Sgr A* Intra-Day Variability between the light curves at 90 and 102 GHz

AbstractWe performed the observation of the flux densities of Sgr A* at 90 and 102 GHz on 6 April 2005 using the Nobeyama Millimeter Array in order to detect the time lag between these frequencies. We constructed light curves covering a few hour with 1 min bin, and the Intra-Day Variability, which had a rising phase and intensity peak, of Sgr A* is clearly seen at both frequencies. We calculated the z-transformed discrete correlation function between the light curves of Sgr A* at 90 and 102 GHz. The derived time lag of the flares at these frequencies was approximately zero, contrary to our expectations based on the previously reported time lag at lower frequencies. If the radio flares of Sgr A* are explained by the expanding plasma model, the light curve at 90 GHz would be delayed with respect to the one at 102 GHz. However, we could not find such a delay with statistical significance in our data.

The long-term optical behavior of BL Lac object S5 0716+714

BL Lac object S5 0716+714 is a well-studied object. In this paper, the available optical (BVRI) data of this source are compiled, and the B-, V-, R- and I-band light curves are constructed. Each of them is analyzed by means of the discrete correlation function (DCF) method, the structure function (SF) method and the z-transformed discrete correlation function (ZDCF) method. The results imply that there is a possible periodic variation of 1211 days in each passband light curve. The source varies violently and complicatedly, and exhibits a brightening trend in the light curves.

Multi-band optical variability of BL Lac object OQ 530

Historical optical data are combined on the BL Lac object OQ 530. Verifying the existence of correlations among the flux variations in different bands serves as an important tool to investigate emission processes. To examine the possible existence of a lag between variations in different optical bands from this source, a statistical analysis is performed through the discrete correlation function (DCF) method and the z-transformed discrete correlation function (ZDCF) method. Monte Carlo simulations called ``flux redistribution/random subset selection'' (FR/RSS) are performed to obtain statistically meaningful values for the cross-correlation time lags and their related uncertainties. The analysis confirms that the variations in different optical light curves are strongly correlated, with zero-lag within the errors. Long term variability of color indexes is also analyzed. The result suggests a strong correlation between color index and brightness. A clear bluer-when-brighter chromatism is found, in the sense that the spectrum steepens as the brightness decreases.

Evolution of optical spectral index and variability properties of S5 0716+714

We analyze the spectral variability and spectral evolution in the optical energy region by using multiband (BVRI) optical observations of S5 0716+714 spanning 1994 to 2005. The spectrum hardens when the source becomes brighter, which is consistent with general BL Lac objects. The spectral evolution parameter implies that the spectral variability is small in optical bands over 10 years. A simple model representing the variability of a synchrotron component can explain the spectral changes. In addition, we employ the z-transformed discrete correlation function (ZDCF) to analyze the optical multiband flux correlation. The long-term light curve behavior reveals that the variability time scales are 3.5 yr in the B-band, 3.3 yr in the V-band, 3.4 yr in the R-band and 3.5 yr in the I-band. The time lags between any two optical bands were not found when considering statistical errors.

Time Delay in QSO 0957+561 From 1984–1999 Optical Data

Photometric optical data of QSO 0957+561 covering the period 1984-1999 are analyzed to discern between the two values of the time delay (417 and 424 days) mostly accepted in the recent literature. The observations, performed by groups from three different institutions—Princeton University, Harvard-Smithsonian Center for Astrophysics, and Instituto de Astrofisica de Canarias—and including new unpublished 1998-1999 data from the IAC80 Telescope, were obtained in five filters (V, R, I, g, and r). The different light curves have been divided into observational seasons, and two restrictions have been applied to calculate the time delay better: (1) points with a strange photometric behavior have been removed, and (2) data sets without large gaps have been selected. Simulated data were generated to test several numerical methods intended to compute the time delay (ΔτAB). The methods giving the best results—the discrete correlation function, δ2, z-transformed discrete correlation function, and linear interpolation—were then applied to real data. A first analysis of the 23 different time delays derived from each technique shows that ΔτAB must be in the interval 420-424 days. From our statistical study, a most probable value of ΔτAB = 422.6 ± 0.6 days is inferred.