Preamble

Vol. 66 No. 5

Sept., 2025

Acta Astronomica Sinica

The Comparison of Long-term Mid-infrared Variability between Broad-line and Narrow-line Seyfert 1 Galaxies

HU Zhi-peng MAO Li-sheng†

(School of Physics and Electronic Information, Yunnan Normal University, Kunming 650500)

Abstract

Using archival data from the Wide-field Infrared Survey Explorer (WISE), we compared the long-term mid-infrared variability amplitude of Broad-line Seyfert 1 (BLSy1) galaxies and Narrow-line Seyfert 1 (NLSy1) galaxies. Additionally, we analyzed the correlation between long-term mid-infrared variability amplitude and common active galactic nucleus parameters, utilizing samples of BLSy1 galaxies, NLSy1 galaxies, and a combined sample of both types. The main results are as follows: (1) The long-term mid-infrared variability amplitude of BLSy1 galaxies is greater than that of NLSy1 galaxies, possibly due to differences in accretion disk structure between the two types. Correlation analysis suggests that the larger variability amplitude in BLSy1 galaxies may also be primarily attributed to differences in Eddington ratio between BLSy1 and NLSy1 galaxies. (2) The long-term mid-infrared variability amplitudes of BLSy1 galaxies, NLSy1 galaxies, and the combined sample show significant negative correlations with 5100 Å luminosity, Eddington ratio, and FeII emission line strength. The long-term mid-infrared variability amplitude of NLSy1 galaxies is significantly positively correlated with [OIII] 5007 emission line strength.

Keywords: galaxies: Seyfert, infrared: variability, radiation mechanisms: thermal radiation, methods: statistical

1 Introduction

Active Galactic Nuclei (AGN) are extragalactic systems with extremely active central regions, powered by accretion onto supermassive black holes (SMBH) located at galaxy centers \cite{1,2}. Their observational characteristics include compact morphology, high luminosity, broad continuum radiation, and strong emission lines. Seyfert galaxies represent a class of lower-luminosity AGN with prominent emission lines in their spectra, such as hydrogen Balmer lines, [OIII] emission lines, and MgII emission lines. Based on spectral features, Seyfert galaxies are primarily divided into two subclasses: Seyfert 1 and Seyfert 2. The former display broad lines including permitted lines (e.g., HI, HeI, or HeII) and narrower forbidden lines (e.g., [OIII]), along with some narrow permitted lines, while the latter show only narrow permitted and forbidden lines \cite{3}. Seyfert 1 galaxies are further classified into Broad-line Seyfert 1 (BLSy1) and Narrow-line Seyfert 1 (NLSy1) based on emission line properties. The original classification criteria for NLSy1 galaxies are: relatively narrow full width at half maximum (FWHM) of the Hβ emission line (FWHM < 2000 km s⁻¹) and weak [OIII] emission line (flux ratio of [OIII] to Hβ < 3) \cite{4,5}, along with high black hole accretion rates. Compared to BLSy1 galaxies, NLSy1 galaxies exhibit stronger FeII radiation \cite{6}, strong soft X-ray excess, rapid X-ray flux variations \cite{7,8,9}, lower black hole masses, and higher Eddington ratios \cite{10,11,12,13,14}. However, the relationship between BLSy1 and NLSy1 galaxies remains unclear. NLSy1 galaxies may represent an early evolutionary stage of AGN, preceding BLSy1 galaxies \cite{15,16,17}, although some studies find similar black hole masses and Eddington ratios between the two types, suggesting their differences arise from geometric structure \cite{18,19}.

Non-periodic variability is ubiquitous in AGN across wavelengths from radio to high-energy bands, with timescales ranging from minutes to years \cite{20}. Variability provides valuable insights into AGN physics, enabling estimation of black hole masses \cite{21,22} and exploration of accretion disk, broad-line region, and dust torus structural characteristics \cite{23,24,25,26,27}. It is also widely used for AGN identification and confirmation \cite{28,29,30}. Various processes have been proposed to explain AGN variability, including accretion disk instabilities, Poisson processes, and starburst models \cite{31,32,33,34}. Therefore, studying variability in BLSy1 and NLSy1 galaxies can illuminate the physical properties of their central black holes and surrounding structures. Long-term variability amplitudes in the UV and optical bands have been extensively compared for BLSy1 and NLSy1 galaxies \cite{35,36,37,38}, revealing that BLSy1 galaxies exhibit greater variability amplitudes than NLSy1 galaxies in these bands. Since UV and optical radiation in AGN primarily originates from the accretion disk, different variability amplitudes may indicate distinct physical processes occurring in the accretion disks of BLSy1 and NLSy1 galaxies \cite{37}. Long-term variability amplitudes in the UV and optical bands have been found to correlate with common AGN parameters, particularly showing negative correlations with 5100 Å luminosity, Eddington ratio, and FeII emission line strength, suggesting that different variability amplitudes may reflect different observational characteristics between BLSy1 and NLSy1 galaxies \cite{35,37,38}.

AGN infrared radiation primarily arises from thermal emission of dust tori heated by UV and optical photons generated by accretion onto the central supermassive black hole \cite{39,40}. While long-term variability behavior in the UV and optical bands has been widely studied for BLSy1 and NLSy1 galaxies, fewer studies have investigated their long-term infrared variability. This paper compares the mid-infrared long-term variability amplitudes of these two galaxy types. According to the standard AGN model, infrared variability amplitude depends on both the amplitude of UV/optical variability and the dust covering factor (CF). Studying mid-infrared variability in these galaxies not only allows comparison with UV/optical variability behavior and provides indirect clues about accretion processes, but also enables analysis of AGN dust torus properties \cite{41,42,43,44}.

Correlation analysis between variability and AGN parameters is an effective method for exploring AGN physics. Previous work \cite{45} found that long-term mid-infrared variability amplitude is negatively correlated with 5100 Å luminosity, Eddington ratio, and FeII emission line strength, but only systematically studied NLSy1 galaxies. This paper analyzes correlations between long-term mid-infrared variability amplitude and common AGN parameters for both BLSy1 and NLSy1 galaxies, and also combines the samples to investigate correlations for Seyfert 1 galaxies as a whole. Compared to UV and optical bands, infrared bands offer unique advantages: in low-redshift AGN, the infrared continuum is less affected by strong emission lines and suffers less from dust extinction \cite{46}.

2.1 Sample

In this work, we utilized the latest Seyfert 1 galaxy catalog provided by \cite{47}, which includes 52,273 BLSy1 galaxies and 22,656 NLSy1 galaxies. This catalog was obtained through detailed decomposition of quasar and galaxy spectra from the Sloan Digital Sky Survey Data Release 17 (SDSS-DR17) using the publicly available software Bayesian AGN Decomposition Analysis for SDSS Spectra. The catalog contains sources detected by FIRST (Faint Images of the Radio Sky at Twenty-Centimeters) with radio emission, including 2,568 BLSy1 galaxies and 730 NLSy1 galaxies \cite{48}. These radio-loud sources constitute relatively small fractions of 4.91% and 3.22% of all BLSy1 and NLSy1 galaxies, respectively. Since synchrotron radiation from jets in radio-loud AGN may significantly contribute to infrared variability, we excluded these radio-detected BLSy1 and NLSy1 galaxies, leaving 49,705 BLSy1 galaxies and 21,926 NLSy1 galaxies.

2.2 WISE Long-term Variability Data

The Wide-field Infrared Survey Explorer (WISE) is equipped with a 40 cm infrared telescope that completed its first all-sky survey in mid-infrared bands in July 2010. Operating at wavelengths of 3.4 μm, 4.6 μm, 12 μm, and 22 μm (W1, W2, W3, and W4 bands) with spatial resolutions of 6.1″, 6.4″, 6.5″, and 12.0″ respectively, WISE completes a full-sky survey every six months with significantly higher sensitivity than previous infrared missions such as IRAS \cite{49}. With NASA funding, the WISE data processing system was improved and renamed NEOWISE (Near-Earth Object Wide-field Infrared Survey Explorer). NEOWISE conducted surveys only in W1 and W2 bands, entering hibernation in February 2011 \cite{50}. In December 2013, NEOWISE resumed operations with original performance, continuing W1 and W2 band surveys as NEOWISE-R \cite{51}, which concluded in July 2024.

To calculate long-term mid-infrared variability of BLSy1 and NLSy1 galaxies, we utilized all NEOWISE-R data from December 2013 to July 2024, spanning approximately 10.6 years. Because W1 band data have higher signal-to-noise ratio than W2 band, we obtained W1 band photometric data for 49,705 BLSy1 galaxies and 21,926 NLSy1 galaxies from the NASA Infrared Science Archive (IRSA) with a search radius of 3″. We then applied necessary data screening, adopting criteria from \cite{52} and \cite{53} to remove poor-quality data: (1) w1rchi2 < 5: the reduced chi-square value of profile-fitting photometry in W1 band is less than 5; (2) nb < 3: the number of point spread functions (PSFs) used in multi-frame pipeline profile fitting is less than 3; (3) cc_flags = 0: no contamination from known image artifacts during photometric or positional measurements in W1 band; (4) qual_frame > 0: frame quality score greater than 0, indicating relatively good image quality and noise characteristics; (5) qi_fact > 0: single-frame image quality factor greater than 0 for photometric or positional measurements in W1 band; (6) saa_sep > 0: angular separation from the South Atlantic Anomaly (SAA) boundary greater than 0, indicating minimal SAA influence; (7) moon_masked = 0: no contamination by lunar scattered light during photometric or positional measurements in W1 band.

We also removed data points where W1 magnitudes were upper limits only. For BLSy1 galaxies, such upper-limit data points numbered 84,143, representing approximately 0.55% of total data points. For NLSy1 galaxies, they numbered 59,571, representing about 0.99%. Details on photometric data quality can be found in the official WISE documentation \cite{54}. After removing poor data, we segmented the observations into epochs, with intervals between epochs corresponding to NEOWISE-R's full-sky coverage time (approximately 180 days). This segmentation yielded observation windows of about 1 day duration each. Following data cleaning and epoch segmentation, 2,040 BLSy1 galaxies (4.10% of the radio-excluded sample) and 1,624 NLSy1 galaxies (7.41%) had 17 or fewer observation windows. To ensure robust analysis of long-term mid-infrared variability amplitudes, we retained only sources with more than 17 observation windows, leaving 47,665 BLSy1 galaxies and 20,302 NLSy1 galaxies.

3.1 Weighted Averaging

Since this study investigates long-term mid-infrared variability of BLSy1 and NLSy1 galaxies, we performed weighted averaging for each observation epoch of the 47,665 BLSy1 and 20,302 NLSy1 galaxies \cite{55,56}. Each epoch's magnitude sequence consists of photometric data points within that epoch. The weighted average magnitude is given by:

$$
m_{\text{wtd}} = \frac{\sum_{i=1}^{N} w_i m_i}{\sum_{i=1}^{N} w_i}
$$

where the corresponding error is:

$$
\sigma_{m_{\text{wtd}}} = \sqrt{\frac{1}{\sum_{i=1}^{N} w_i}}
$$

with weights defined as $w_i = 1/\sigma_i^2$. The standard error of the weighted mean is:

$$
\sigma_{m_{\text{wtd}}} = \sqrt{\frac{\sum_{i=1}^{N} w_i m_i^2}{\sum_{i=1}^{N} w_i} - m_{\text{wtd}}^2}
$$

To illustrate the resulting long-term variability data, we present light curves for two sources as examples. FIGURE:1 and FIGURE:1 show the long-term mid-infrared light curves for the BLSy1 galaxy SDSS J000115.88+051902.0 and the NLSy1 galaxy SDSS J144619.29+005317.9, respectively.

3.2 Long-term Variability Amplitude

To characterize long-term mid-infrared variability of BLSy1 and NLSy1 galaxies, we performed variance analysis on each light curve and subtracted observational uncertainties to calculate the variability amplitude $\sigma_m$ for the retained samples \cite{57,58,59}:

$$
\sigma_m = \sqrt{\frac{1}{N_{\text{ep}}-1} \sum_{i=1}^{N_{\text{ep}}} (m_i - m_{\text{wtd}})^2}
$$

where $N_{\text{ep}}$ is the number of observation epochs for each source, $m_i$ is the magnitude in each epoch, and $m_{\text{wtd}}$ is the weighted average magnitude across all epochs for each source. The uncertainty $\epsilon$ is defined as:

$$
\epsilon^2 = \frac{1}{N_{\text{ep}}} \sum_{i=1}^{N_{\text{ep}}} \epsilon_i^2 + \epsilon_s^2
$$

where $\epsilon_i$ is the uncertainty in each epoch and $\epsilon_s$ is the systematic uncertainty. For the W1 band, the systematic uncertainty is 0.024 mag \cite{60}. The final variability amplitude is:

$$
\sigma_m = \begin{cases}
\sqrt{\sigma^2 - \epsilon^2} & \text{if } \sigma > \epsilon \
0 & \text{otherwise}
\end{cases}
$$

where $\sigma$ is the standard deviation of the light curve and $\epsilon$ is the total uncertainty.

4.1 Mid-infrared Variability of BLSy1 and NLSy1 Galaxies

Using the above method, we calculated long-term mid-infrared variability amplitudes for 47,665 BLSy1 galaxies and 20,302 NLSy1 galaxies. In the BLSy1 sample, 3,059 sources (6.42%) had $\sigma_m = 0$, while 44,606 had $\sigma_m \neq 0$. In the NLSy1 sample, 2,274 sources (11.20%) had $\sigma_m = 0$, while 18,028 had $\sigma_m \neq 0$. A value of $\sigma_m = 0$ may indicate minimal variability in these sources. [FIGURE:2] shows the cumulative probability distribution of $\sigma_m$ for all BLSy1 and NLSy1 galaxies. The figure demonstrates that BLSy1 galaxies exhibit greater long-term mid-infrared variability amplitude than NLSy1 galaxies. We calculated mean values of 0.088 mag for BLSy1 galaxies and 0.086 mag for NLSy1 galaxies. Additionally, we computed median values with upper and lower errors, obtaining $0.074^{+0.053}{-0.040}$ mag for BLSy1 galaxies and $0.069^{+0.053}$ mag for NLSy1 galaxies. The median values also indicate greater long-term mid-infrared variability amplitude in BLSy1 galaxies.

To further verify this difference, we performed Kolmogorov-Smirnov (K-S) and Mann-Whitney rank-sum tests on the $\sigma_m$ distributions of BLSy1 and NLSy1 galaxies. The K-S test yields a D statistic of 0.057 with a chance probability P-value of $4.262 \times 10^{-40}$. The rank-sum test gives a U statistic of $5.198 \times 10^8$ with P-value $2.384 \times 10^{-53}$. The D statistic represents the maximum vertical difference between the two cumulative distribution functions, while the P-value indicates the probability of observing the current or more extreme data under the null hypothesis, and the U statistic measures the difference in rank sums between the two groups. The K-S test D statistic confirms that BLSy1 galaxies have greater long-term mid-infrared variability amplitude than NLSy1 galaxies, while the P-value shows that the $\sigma_m$ distributions differ significantly. The large U statistic and small P-value from the rank-sum test also confirm significantly different distributions. Thus, BLSy1 galaxies show greater long-term variability amplitude than NLSy1 galaxies in the W1 band, consistent with UV and optical band comparisons \cite{35,36,37,38,61}.

4.2 Mid-infrared Variability of BLSy1 and NLSy1 Galaxy Subsamples

In AGN variability studies, brighter sources are more likely to have detectable small-amplitude variations. To avoid bias from differences in infrared brightness distributions, we performed redshift-W1 band luminosity two-dimensional matching for the 47,665 BLSy1 and 20,302 NLSy1 galaxies. This matching ensures similar brightness distributions between the final BLSy1 and NLSy1 samples. To calculate each source's W1 band luminosity, we first converted all W1 band magnitudes to flux densities using:

$$
F_\nu = F_{\nu,0} \times 10^{-m_{\text{Vega}}/2.5}
$$

where $F_\nu$ is the flux density at a given frequency, $F_{\nu,0}$ is the zero-magnitude flux density (309.54 Jy for W1), and $m_{\text{Vega}}$ is the observed magnitude in the Vega system. We then averaged flux densities across each observation epoch and represented each source's W1 band flux density as the mean across all epochs. Finally, we calculated W1 band luminosity using $L_{W1} = 4\pi d_L^2 L_\nu$, where $L_\nu = F_\nu c/\lambda^2$, $d_L$ is the luminosity distance, $\lambda$ is the wavelength, and $c$ is the speed of light in vacuum. Cosmological parameters consistent with \cite{47} were adopted.

[TABLE:1] and [TABLE:2] list basic information for BLSy1 and NLSy1 galaxies, respectively, including their $\sigma_m$, W1 band luminosity, and other parameters. After calculating each source's W1 band luminosity, we set redshift and W1 band luminosity bin sizes of 0.002 and 0.01 dex, respectively. We performed nearest-neighbor matching within the redshift-W1 band luminosity plane, obtaining 9,323 BLSy1 galaxies and 9,323 NLSy1 galaxies as subsamples. [FIGURE:3] shows the distribution of these matched subsamples in the redshift-W1 band luminosity plane. The top panel displays the redshift distribution, while the right panel shows the W1 band luminosity distribution. A two-dimensional K-S test on the redshift and W1 band luminosity distributions yields D = 0.00091 and P = 1, indicating no significant differences between the BLSy1 and NLSy1 subsample distributions \cite{62,63}.

To compare mid-infrared variability of the 9,323 BLSy1 and 9,323 NLSy1 galaxies, we calculated their $\sigma_m$. [FIGURE:4] shows the cumulative probability distribution of $\sigma_m$ for these subsamples, including 733 BLSy1 galaxies (7.86%) and 1,068 NLSy1 galaxies (11.46%) with $\sigma_m = 0$. The figure clearly demonstrates that BLSy1 galaxies exhibit greater long-term mid-infrared variability amplitude than NLSy1 galaxies. Mean values are 0.090 mag for BLSy1 galaxies and 0.083 mag for NLSy1 galaxies. Median values with errors are $0.075^{+0.054}{-0.042}$ mag for BLSy1 galaxies and $0.066^{+0.050}$ mag for NLSy1 galaxies. Both median and mean values confirm greater variability amplitude in BLSy1 galaxies.

We performed K-S and rank-sum tests on the $\sigma_m$ distributions of these subsamples. The K-S test yields D = 0.085 with P-value $1.322 \times 10^{-29}$, while the rank-sum test gives U = $4.849 \times 10^7$ with P-value $9.380 \times 10^{-43}$. These results confirm that BLSy1 galaxy subsamples have significantly greater long-term mid-infrared variability amplitude than NLSy1 galaxy subsamples, with significantly different distributions. Therefore, even after controlling for redshift and W1 band luminosity, BLSy1 galaxies show greater long-term mid-infrared variability amplitude than NLSy1 galaxies.

4.3 Effect of Dust Covering Factor on Mid-infrared Variability

Since mid-infrared variability amplitude in BLSy1 and NLSy1 galaxies may be influenced by dust covering factor, with larger covering factors tending to exhibit greater mid-infrared variability, we calculated W1 band dust covering factors for 47,665 BLSy1 and 20,302 NLSy1 galaxies using the ratio of W1 band luminosity to bolometric luminosity \cite{64,65}. Bolometric luminosity data were also obtained from the catalog provided by \cite{47}, which calculates $L_{\text{bol}} = 9.26 \times L_\nu(5100\text{ Å})$ (erg s⁻¹), representing the total radiation intensity across all wavelengths. We found average W1 band dust covering factors of 0.462 for BLSy1 galaxies and 0.526 for NLSy1 galaxies. Median values are $0.329^{+0.379}{-0.136}$ for BLSy1 galaxies and $0.351^{+0.484}$ for the rank-sum test, confirming significantly different distributions.}$ for NLSy1 galaxies. Both mean and median values indicate larger dust covering factors in NLSy1 galaxies. K-S and rank-sum tests on the two samples yield D = 0.055, P = $2.067 \times 10^{-37}$ for the K-S test and U = $4.546 \times 10^8$, P = $1.005 \times 10^{-35

Because the W2 band may be closer to the spectral energy distribution (SED) peak of dust torus infrared emission, we also calculated W2 band dust covering factors for better comparison. Using the same quality screening criteria as for W1, we retained 46,782 BLSy1 and 18,965 NLSy1 galaxies with more than 17 observation windows. Statistical analysis yields average and median W2 band dust covering factors of 0.599 and $0.433^{+0.467}{-0.175}$ for BLSy1 galaxies, and 0.675 and $0.454^{+0.591}$, respectively, indicating significantly different distributions.}$ for NLSy1 galaxies. These results again show larger dust covering factors in NLSy1 galaxies, consistent with W1 band findings. K-S and rank-sum tests on W2 band dust covering factors give D = 0.049, P = $9.807 \times 10^{-29}$ and U = $4.237 \times 10^8$, P = $1.971 \times 10^{-19

We performed similar analysis on W1 band dust covering factors for the redshift- and luminosity-matched subsamples. The BLSy1 subsample has average and median W1 band dust covering factors of 0.495 and $0.356^{+0.435}{-0.152}$, while the NLSy1 subsample has 0.527 and $0.346^{+0.464}$. Mean and median values show no significant difference. K-S and rank-sum tests on these subsamples yield D = 0.021, P = 0.032 and U = $4.380 \times 10^7$, P = 0.349, respectively, indicating no significant difference in W1 band dust covering factor distributions between the subsamples.

These results suggest that dust covering factor is likely not the primary cause of greater long-term mid-infrared variability amplitude in BLSy1 galaxies compared to NLSy1 galaxies. The difference in variability amplitude between these two galaxy types may therefore originate mainly from the accretion disk. However, this represents only a rough estimate of dust covering factor, and more systematic estimates require deeper future investigation.

4.4 Relationship with AGN Parameters

This section investigates correlations between W1 band long-term variability amplitude and various AGN parameters for 44,606 BLSy1 galaxies and 18,028 NLSy1 galaxies using linear regression methods. The parameters examined include 5100 Å luminosity \cite{47}, black hole mass \cite{47}, Eddington ratio \cite{66}, FWHM of the broad Hβ emission line component \cite{47}, FeII emission line strength \cite{47}, and [OIII] 5007 emission line strength \cite{47}. The 5100 Å luminosity represents radiation intensity at 5100 Å. The Eddington ratio, describing AGN accretion rate, is defined as the ratio of bolometric luminosity to Eddington luminosity: $R_{\text{Edd}} = L_{\text{bol}}/L_{\text{Edd}}$, where $L_{\text{Edd}} = 1.3 \times 10^{38} M_{\text{BH}}/M_\odot$ (erg s⁻¹). FeII emission line strength is defined as the flux ratio of FeII lines (4434–4684 Å) to broad Hβ emission: $R_{4570} = f(\text{FeII}(4434-4684))/f(\text{Hβ})$ \cite{67}. [OIII] 5007 emission line strength is defined as the flux ratio of [OIII] 5007 to narrow Hβ: $R_{5007} = f(\text{[OIII] 5007})/f(\text{Hβ})$ \cite{68}. Following \cite{35,37,38}, correlation analyses were performed in logarithmic space, excluding sources with $\sigma_m = 0$ (numbers given in Section 4.1).

We performed least-squares linear fitting between $\sigma_m$ and these AGN parameters for BLSy1 galaxies, NLSy1 galaxies, and the combined sample. We also calculated equal-density distributions and scatter plots, and computed Spearman correlation coefficients and chance probability P-values for each sample. [TABLE:3] presents all correlation results. AGN parameter data were obtained by matching our 44,606 BLSy1 and 18,028 NLSy1 galaxies with the catalog from \cite{47}.

4.4.1 Relationship with 5100 Å Luminosity, Black Hole Mass, and Eddington Ratio

[FIGURE:5] shows the relationship between long-term mid-infrared variability amplitude and 5100 Å luminosity and black hole mass for BLSy1 galaxies, NLSy1 galaxies, and the combined sample. FIGURE:5 reveals significant negative correlations between $\sigma_m$ and 5100 Å luminosity for both BLSy1 and NLSy1 galaxies, as well as for the combined sample. These significant negative correlations are confirmed by Spearman correlation coefficients and P-values in [TABLE:3], consistent with optical band studies of BLSy1 and NLSy1 galaxies \cite{38}. This negative correlation is not limited to Seyfert galaxies but also appears in studies of other AGN types \cite{69,70,71,72}. Black hole masses in the \cite{47} sample were estimated using virialization of broad-line region clouds \cite{22}. FIGURE:5 shows no significant correlation between long-term mid-infrared variability amplitude and black hole mass for BLSy1 galaxies, NLSy1 galaxies, or the combined sample. Previous work \cite{35} found that variability amplitude's dependence on black hole mass disappears when accounting for its dependence on Eddington ratio.

[FIGURE:6] presents the relationship between long-term mid-infrared variability amplitude and Eddington ratio and FWHM of Hβ emission line. FIGURE:6 shows clear negative correlations between $\sigma_m$ and Eddington ratio for BLSy1 galaxies, NLSy1 galaxies, and the combined sample, quantified by linear regression in [TABLE:3}. Reference \cite{45} found this same negative correlation in NLSy1 galaxies, while \cite{35} reported significant negative correlations between long-term variability amplitude and Eddington ratio in UV and optical bands for BLSy1, NLSy1, and combined samples. This correlation has also been found in many quasar studies \cite{69,70,71,73}.

4.4.2 Correlation with Emission Line Parameters

This section examines relationships between long-term mid-infrared variability amplitude and FWHM of broad Hβ component, FeII emission line strength, and [OIII] 5007 emission line strength for BLSy1 galaxies, NLSy1 galaxies, and the combined sample. Typically, narrow Hβ and [OIII] 5007 emission originate from the narrow-line region, while broad Hβ and FeII emission come from the broad-line region. FIGURE:6 and [TABLE:3] show no significant correlation between $\sigma_m$ and FWHM of Hβ for any sample. [FIGURE:7] displays the relationship between $\sigma_m$ and FeII and [OIII] 5007 emission line strengths. FIGURE:7 reveals significant negative correlations between $\sigma_m$ and FeII emission line strength for all three samples, confirmed by Spearman correlation coefficients. FIGURE:7 and [TABLE:3] show a significant positive correlation between $\sigma_m$ and [OIII] 5007 emission line strength for NLSy1 galaxies, but no significant correlation for BLSy1 galaxies or the combined sample. Reference \cite{45} found a significant negative correlation between NLSy1 galaxies' long-term mid-infrared variability amplitude and $R_{4570}$. Studies \cite{35,37} reported significant positive correlations between UV/optical variability amplitude and FWHM of Hβ, and significant negative correlations with $R_{4570}$. Reference \cite{35} also found significant positive correlations between long-term variability amplitude and $R_{5007}$ in UV and optical bands. The mid-infrared variability amplitude correlations with these emission line parameters are consistent with UV/optical band results, though the mid-infrared correlations are weaker.

4.4.3 Influence of AGN Parameters on Variability Differences

The previous sections analyzed correlations between $\sigma_m$ and six common AGN parameters for BLSy1 and NLSy1 galaxies. While differences in $\sigma_m$ between the two types may result from different parameter values, the most relevant parameter remains unclear. Based on the parameter distributions and Spearman correlation analysis, the difference in $\sigma_m$ between the two galaxy types may be most closely related to Eddington ratio. We therefore controlled for Eddington ratio and analyzed correlations between $\sigma_m$ and $R_{4570}$ \cite{74}, and controlled for $R_{4570}$ to analyze correlations between $\sigma_m$ and Eddington ratio. [TABLE:4] presents correlations under these constraints. After fixing Eddington ratio, the negative correlation between $\sigma_m$ and $R_{4570}$ weakens for BLSy1 galaxies but remains significant for NLSy1 galaxies. After fixing $R_{4570}$, both BLSy1 and NLSy1 galaxies show significant negative correlations between $\sigma_m$ and Eddington ratio. The correlation coefficient between variability amplitude and Eddington ratio is larger when $R_{4570}$ is fixed than when Eddington ratio is fixed. These results suggest that the difference in variability amplitude between the two galaxy types is most likely related to Eddington ratio.

5 Summary and Discussion

This paper compared long-term mid-infrared variability amplitudes of 47,665 BLSy1 galaxies and 20,302 NLSy1 galaxies, as well as matched subsamples in redshift-W1 band luminosity. Cumulative probability distributions show that BLSy1 galaxies have greater long-term mid-infrared variability amplitude than NLSy1 galaxies, confirmed by K-S and rank-sum tests. The lower variability amplitude in NLSy1 galaxies may be due to their narrower Hβ emission line widths, lower black hole masses, higher Eddington ratios, and stronger FeII emission line strengths compared to BLSy1 galaxies. NLSy1 galaxies being in an early evolutionary stage may contribute to these parameter differences \cite{36,37}. The difference in variability amplitude between BLSy1 and NLSy1 galaxies in UV and optical bands has been attributed to different physical processes in their accretion disks, which may arise from structural differences. Since mid-infrared radiation primarily originates from thermal emission of dust tori heated by UV/optical photons, differences caused by accretion disks may be reflected in the dust tori, leading to different mid-infrared variability amplitudes.

Although jet synchrotron radiation may contribute to mid-infrared emission, we excluded radio-detected BLSy1 and NLSy1 galaxies, so jet contributions are not considered. Besides these factors, dust covering factor may affect infrared variability amplitude, with larger covering factors typically producing greater amplitude. However, our sample does not show larger W1 or W2 band dust covering factors in BLSy1 galaxies compared to NLSy1 galaxies, suggesting dust covering factor has minimal impact on the comparison results. The variability amplitude difference likely originates primarily from the accretion disk.

We also analyzed correlations between long-term mid-infrared variability amplitude and common AGN parameters for BLSy1 galaxies, NLSy1 galaxies, and their combined sample. We found significant correlations, particularly negative correlations with 5100 Å luminosity, Eddington ratio, and FeII emission line strength. These three negative correlations were previously reported \cite{45}, and \cite{75} found that fainter AGN show greater long-term mid-infrared variability amplitude than brighter ones on 10-year timescales. Many studies have found significant negative correlations between UV/optical variability amplitude and 5100 Å luminosity, Eddington ratio, and FeII emission line strength \cite{35,36,37,38,69,70,71,72}. The negative correlation between UV/optical variability amplitude and Eddington ratio can be understood through the standard geometrically thin, optically thick accretion disk model \cite{76}. Since radiation originates in the inner disk and weakens as it propagates outward, the radius of the emission region at a given wavelength increases with Eddington ratio \cite{45}, as shown by $r \propto T^{-4/3} \propto (\dot{m}/M_{\text{BH}})^{1/3} L_{\text{bol}}^{4/3}$. For a given wavelength, UV/optical variability amplitude decreases with increasing Eddington ratio \cite{77}. Due to the relationship between mid-infrared and UV/optical radiation, the negative correlation between long-term mid-infrared variability amplitude and Eddington ratio may also be influenced by this relationship.

References \cite{78,79,80} suggest that Eddington ratio may be the underlying driver of correlations between variability amplitude and emission line parameters. We found significant negative correlations between long-term mid-infrared variability amplitude and both FeII emission line strength and Eddington ratio, suggesting that the correlation with FeII emission line strength may be influenced by Eddington ratio. By controlling for Eddington ratio and FeII emission line strength, we conclude that Eddington ratio is most likely the parameter responsible for differences in long-term mid-infrared variability amplitude between BLSy1 and NLSy1 galaxies. Compared to UV and optical band studies, our mid-infrared variability amplitude comparison yields consistent results, and correlations with common AGN parameters are also found. However, mid-infrared variability amplitude correlations with AGN parameters are weaker than in UV and optical bands, possibly because UV and optical radiation is partially obscured by the dust torus, weakening the variability signal and consequently reducing mid-infrared variability amplitude. Our results therefore support the scenario where mid-infrared radiation originates from thermal emission of dust tori heated by UV/optical radiation from the accretion disk.

Acknowledgments

We thank the referee for valuable suggestions that significantly improved the manuscript. We acknowledge the data provided by the Wide-field Infrared Survey Explorer.

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