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Sina Taamoli

Publications and source records attributed to Sina Taamoli.

16 recordsLinked to original sources
arXiv2026

COSMOS-Web galaxy groups: Evolution of red sequence and quiescent galaxy fraction

We investigate the redshift and group richness dependence of the quiescent fraction and red-sequence (RS) parameters in COSMOS galaxy groups from z=0 to z=3.7. We analyzed the deep and well-characterized sample of groups detected with AMICO in the COSMOS(-Web) field. Our study of the quiescent galaxy population is based on a machine-learning classification tool based on rest-frame magnitudes. The algorithm learns from several traditional methods to estimate the probability of a galaxy being quiescent, achieving high precision and recall. Starting from this classification, we computed quiescent galaxy fractions within groups via two methods: one based on the membership probabilities provided by AMICO, which rely on an analytical model, and another using a model-independent technique. We then detected the RS by estimating the ridgeline position using photometric data, followed by sigma clipping to remove outliers. This analysis was performed using both rest-frame and observed-frame magnitudes with rest-frame matching. We compared the results from both approaches and investigated the $z$ and richness dependence of the RS parameters. We found that the quiescent galaxy population in groups builds up steadily from z=1.5-2 across all richnesses, with faster and earlier growth in the richest groups. The first galaxies settle onto the RS ridgeline by $z \sim 2$, consistent with current evolutionary scenarios. Notably, we reported a rare overdensity of quiescent galaxies at z=3.4, potentially one of the most distant early RSs observed. Extending our study to X-rays, we found that X-ray faint groups have, on average, lower quiescent fractions than X-ray bright ones, likely reflecting their typical location in filaments. Leveraging the broad wavelength coverage of COSMOS2025, we traced RS evolution over $\sim 12$ Gyr, finding no significant trends in either slope or scatter of the ridgeline.

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arXiv2026

COSMOS-Web: Estimating Physical Parameters of Galaxies Using Self-Organizing Maps

The COSMOS-Web survey, with its unparalleled combination of multiband data, notably, near-infrared imaging from JWST's NIRCam (F115W, F150W, F277W, and F444W), provides a transformative dataset down to $\sim28$ mag (F444W) for studying galaxy evolution. In this work, we employ Self-Organizing Maps (SOMs), an unsupervised machine learning method, to estimate key physical parameters of galaxies -- redshift, stellar mass, star formation rate (SFR), specific SFR (sSFR), and age -- directly from photometric data out to $z=3.5$. SOMs efficiently project high-dimensional galaxy color information onto 2D maps, showing how physical properties vary among galaxies with similar spectral energy distributions. We first validate our approach using mock galaxy catalogs from the HORIZON-AGN simulation, where the SOM accurately recovers the true parameters, demonstrating its robustness. Applying the method to COSMOS-Web observations, we find that the SOM delivers robust estimates despite the increased complexity of real galaxy populations. Performance metrics ($σ_{\mathrm{NMAD}}$ typically between $0.1$--$0.3$, and Pearson correlation between $0.7$ and $0.9$) confirm the precision of the method, with $\sim$ $70\%$ of predictions within 1$σ$ dex of reference values. Although redshift estimation in COSMOS-Web remains challenging (median $σ_{\mathrm{NMAD}} = 0.04$), the overall success of the highlights its potential as a powerful and interpretable tool for galaxy parameter estimation. A key advance of this work is the use of JWST/NIRCam photometry, particularly the F444W band, which enhances SOM training and allows more accurate estimation of stellar mass, SFR, and age compared to previous studies using IRAC/Spitzer filters.

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arXiv2025

Large-Scale Structure in COSMOS-Web: Tracing Galaxy Evolution in the Cosmic Web up to $z \sim 7$ with the Largest JWST Survey

We present a reconstruction of the large-scale structure using the James Webb Space Telescope's (JWST) COSMOS-Web program to trace environmentally driven galaxy evolution up to $z\sim7$. We applied a weighted kernel density estimation method to 160,000 galaxies with robust photometric redshifts. We find that stellar mass has a positive correlation with density at all redshifts, stronger for quiescent galaxies (QGs) at $z\lesssim2.5$, while at higher redshifts ($2.5\lesssim z\lesssim5.5$) this trend is confined to extreme overdense environments, consistent with early mass assembly in proto-clusters. The star-formation rate (SFR) shows a negative trend with density for QGs at $z\lesssim1.2$, reversing at $z\gtrsim1.8$, while star-forming galaxies (SFGs) show a mild positive correlation up to $z\sim5.5$. The specific SFR remains nearly flat for SFGs and declines with density for QGs at $z\lesssim1.2$. Moreover, mass and environmental quenching efficiencies show that mass-driven processes dominate at $z\gtrsim2.5$, the two processes act with comparable strength between $0.8\lesssim z\lesssim2.5$, and environmental quenching becomes stronger for low-mass galaxies ($M_\star\lesssim10^{10} M_\odot$) at $z\lesssim0.8$. These findings reveal that large-scale structure drives galaxy evolution by enhancing early mass assembly in dense regions and increasingly suppressing star formation in low-mass systems at later times, establishing the environmental role of the cosmic web across cosmic history. COSMOS-Web, the largest JWST survey, provides accurate and deep photometric redshifts, reaching 80% mass completeness at $\log(M_\star/M_\odot)\sim8.7$ at $z\sim7$, enabling the first view of how environments shaped galaxy evolution from the epoch of reionization to the present day.

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arXiv2025

COSMOS Spectroscopic Redshift Compilation (First Data Release): 488k Redshifts Encompassing Two Decades of Spectroscopy

We present the COSMOS Spectroscopic Redshift Compilation encompassing ~ 20 years of spectroscopic redshifts within a 10 deg$^2$ area centered on the 2 deg$^2$ COSMOS legacy field. This compilation contains 487,666 redshifts of 266,284 unique objects from 138 individual observing programs up to $z \sim 8$ with median stellar mass $\sim 10^{8.4}$ to $10^{10}$ M$_\odot$ (redshift dependent). Rest-frame $NUVrJ$ colors and SFR -- stellar mass correlations show the compilation primarily contains low- to intermediate-mass star-forming and massive, quiescent galaxies at $z < 1.25$ and mostly low-mass bursty star-forming galaxies at $z > 2$. Sources in the compilation cover a diverse range of environments, including protoclusters such as ``Hyperion''. The full compilation is 50\% spectroscopically complete by $i \sim 23.4$ and $K_s \sim 21.6$ mag; however, this is redshift dependent. Spatially, the compilation is $>50$\% ($>30$\%) complete within the central (outer) region limited to $i < 24$ mag and $K_s < 22.5$ mag, separately. We demonstrate how the compilation can be used to validate photometric redshifts and investigate calibration metrics. By training self-organizing maps on COSMOS2020/Classic and projecting the compilation onto it, we find key galaxy subpopulations that currently lack spectroscopic coverage including $z < 1$ intermediate-mass quiescent galaxies and low-/intermediate-mass bursty star-forming galaxies, $z \sim 2$ massive quiescent galaxies, and $z > 3$ massive star-forming galaxies. This highlights how combining self-organizing maps with our compilation can provide guidance for future spectroscopic observations to get a complete spectroscopic view of galaxy populations. Lastly, the compilation will undergo periodic data releases that incorporate new spectroscopic redshift measurements, providing a lasting legacy resource for the community.

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arXiv2025

COSMOS Web: Morphological quenching and size-mass evolution of brightest group galaxies from z = 3.7

We present a comprehensive study of the structural evolution of Brightest Group Galaxies (BGGs) from redshift $z \simeq 0.08$ to $z = 3.7$ using the \textit{James Webb Space Telescope}'s 255h COSMOS-Web program. This survey provides deep NIRCam imaging in four filters (F115W, F150W, F277W, F444W) across $\sim 0.54~\mathrm{deg}^2$ and MIRI coverage in $\sim 0.2~\mathrm{deg}^2$ of the COSMOS field. High-resolution NIRCam imaging enables robust size and morphological measurements, while multiwavelength photometry yields stellar masses, SFRs, and Sérsic parameters. We classify BGGs as star-forming and quiescent using both rest-frame NUV--$r$--$J$ colors and a redshift-dependent specific star formation rate (sSFR) threshold. Our analysis reveals: (1) quiescent BGGs are systematically more compact than their star-forming counterparts and exhibit steeper size--mass slopes; (2) effective radii evolve as $R_e \propto (1+z)^{-α}$, with $α= 1.11 \pm 0.07$ (star-forming) and $1.40 \pm 0.09$ (quiescent); (3) star formation surface density ($Σ_{\mathrm{SFR}}$) increases with redshift and shows stronger evolution for massive BGGs ($\log_{10}(M_\ast/M_\odot) \geq 10.75$); (4) in the $Σ_*$--sSFR plane, a structural transition marks the quenching process, with bulge-dominated systems comprising over 80\% of the quiescent population. These results highlight the co-evolution of structure and star formation in BGGs, shaped by both internal and environmental processes, and establish BGGs as critical laboratories for studying the baryonic assembly and morphological transformation of central galaxies in group-scale halos.

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arXiv2025

The COSMOS-Web deep galaxy group catalog up to $z=3.7$

Galaxy groups with $M_{tot} \lesssim 10^{14}$ $M_\odot$ and up to a few tens of members are the most common galaxy environment, marking the transition between field and massive clusters. Identifying groups plays a crucial role in understanding structure formation and galaxy evolution. Modern deep surveys allow us to build well-characterized samples of groups up to the regime where structures were taking shape. We aimed to build the largest deep catalog of galaxy groups to date over the COSMOS-Web field effective area of 0.45 deg$^2$, leveraging the deep high quality data of the new COSMOS-Web photometric catalog resulted from the James Webb Space Telescope observations of the COSMOS-Web field. We performed the group search with the AMICO algorithm, a linear matched filter based on an analytical model for the group signal. AMICO has already been tested in wide and deep field surveys, including COSMOS data up to $z=2$. In this work, we tested the algorithm performances at even higher redshift and searched for protocluster cores at $z>2$. We compiled a list of known protoclusters in COSMOS at $2 \leq z \leq 3.7$, matched them with our detections and studied the clustering of the detected cores. We estimated purity and completeness of our sample by creating data-driven mocks with the SinFoniA code and linked signal-to-noise to purity. We detected 1678 groups in the COSMOS-Web field up to $z=3.7$, including lists of members extending nearly two magnitudes deeper than the previous AMICO-COSMOS catalog. 756 groups were detected with purity of 80\%. More than 500 groups have their redshift confirmed by assigning spectroscopic counterparts. This group catalog offers a unique opportunity to explore galaxy evolution in different environments spanning $\sim$12 Gyr and to study groups, from the least rich population to the formation of the most massive clusters.

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arXiv2025

COSMOS2025: The COSMOS-Web galaxy catalog of photometry, morphology, redshifts, and physical parameters from JWST, HST, and ground-based imaging

We present COSMOS2025, the COSMOS-Web catalog of photometry, morphology, photometric redshifts and physical parameters for more than 700,000 galaxies in the Cosmic Evolution Survey (COSMOS) field. This catalog is based on our \textit{James Webb Space Telescope} 255\,h COSMOS-Web program, which provides deep near-infrared imaging in four NIRCam (F115W, F150W, F277W, F444W) and one MIRI (F770W) filter over the central $\sim 0.54 {\, \rm deg}^2$ ($\sim 0.2 {\, \rm deg}^2$ for MIRI) in COSMOS. These data are combined with ground- and space-based data to derive photometric measurements of NIRCam-detected sources using both fixed-aperture photometry (on the space-based bands) and a profile-fitting technique on all 37 bands spanning 0.3-8 micron. We provide morphology for all sources from complementary techniques including profile fitting and machine-learning classification. We derive photometric redshifts, physical parameters and non-parametric star formation histories from spectral energy distribution (SED) fitting. The catalog has been extensively validated against previous COSMOS catalogs and other surveys. Photometric redshift accuracy measured using spectroscopically confirmed galaxies out to $z\sim9$ reaches $σ_{\rm MAD} = 0.012$ at $m_{\rm F444W}<28$ and remains at $σ_{\rm MAD} \lesssim 0.03$ as a function of magnitude, color, and galaxy type. This represents a factor of $\sim 2$ improvement at 26 AB mag compared to COSMOS2020. The catalog is approximately 80\% complete at $\log(M_{\star}/{\rm M}_{\odot}) \sim 9$ at $z \sim 10$ and at $\log(M_{\star}/{\rm M}_{\odot}) \sim 7$ at $z \sim 0.2$, representing a gain of 1\,dex compared to COSMOS2020. COSMOS2025 represents the definitive COSMOS-Web catalog. It is provided with complete documentation, together with redshift probability distributions, and it is ready for scientific exploitation today.

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arXiv2025

Galaxy Rest-Frame UV Colors at z ~ 2-4 with HST UVCANDELS

We present an analysis of rest-frame UV colors of 17,243 galaxies at $z\sim2-4$ in the HST UVCANDELS fields: GOODS-N, GOODS-S, COSMOS, and EGS. Here, we study the rest-frame UV spectral slope, $β$, measured via model spectra obtained via spectral energy distribution (SED) fitting, $β_{SED}$, and explore its correlation with various galaxy parameters (photometric redshift, UV magnitude, stellar mass, dust attenuation, star formation rate [SFR], and specific SFR) obtained via SED fitting with Dense Basis. We also obtain measurements for $β$ via photometric power-law fitting and compare them to our SED-fit-based results, finding good agreement on average. While we find little evolution in $β$ with redshift from $z=2-4$ for the full population, there are clear correlations between $β$ (and related parameters) when binned by stellar mass. For this sample, lower stellar mass galaxies (log[$M_*$] = 7.5-8.5 $M_\odot$) are typically bluer ($β_{SED}=-2.0\pm 0.2$ / $β_{PL} = -2.1\pm0.4$), fainter ($MUV = -17.8^{+0.7}_{-0.6}$) less dusty ($A{v}=0.4\pm0.1$ mag), exhibit lower rates of star formation (log[SFR]=$0.1\pm0.2 M_\odot/$ yr) and higher specific star formation rates (log[sSFR]=$-8.2\pm0.2 \ \mathrm{yr}^{-1}$) than their high-mass counterparts. Higher-mass galaxies (log[$M_*$] $=10.0-12.0 \ M_\odot$) are on average redder ($β_{SED}=-0.9^{+0.8}_{-0.5}$ / $β_{PL}=-1.0^{+0.8}_{-0.5}$), brighter ($MUV=-19.6^{+1.0}_{-1.2}$), dustier ($Av = 0.9^{+0.5}_{-0.4}$ mag), have higher SFRs (log[SFR]=$1.2^{+0.6}_{-1.1} M_\odot$ yr), and lower sSFRs (log[sSFR]=$-9.1^{+0.5}_{-1.1} {yr}^{-1}$). This study's substantial sample size provides a benchmark for demonstrating that the rest-frame UV spectral slope correlates with stellar mass-dependent galaxy characteristics at $z\sim2-4$, a relationship less discernible with smaller datasets typically available at higher redshifts.

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arXiv2024

COSMOS2020: Disentangling the Role of Mass and Environment in Star Formation Activity of Galaxies at $0.4<z<4$

The role of internal and environmental factors in the star formation activity of galaxies is still a matter of debate, particularly at higher redshifts. Leveraging the most recent release of the COSMOS catalog, COSMOS2020, and density measurements from our previous study we disentangle the impact of environment and stellar mass on the star formation rate (SFR), and specific SFR (sSFR) of a sample of $\sim 210,000$ galaxies within redshift range $0.4< z < 4$ and present our findings in three cosmic epochs: 1) out to $z\sim 1$, the average SFR and sSFR decline at extremely dense environments and high mass end of the distribution which is mostly due to the presence of the massive quiescent population; 2) at $1<z<2$, the environmental dependence diminishes, while mass is still the dominant factor in star formation activity; 3) beyond $z\sim 2$, our sample is dominated by star-forming galaxies and we observe a reversal of the trends seen in the local universe: the average SFR increases with increasing environmental density. Our analysis shows that both environmental and mass quenching efficiencies increase with stellar mass at all redshifts, with mass being the dominant quenching factor in massive galaxies compared to environmental effects. At $2<z<4$, negative values of environmental quenching efficiency suggest that the fraction of star-forming galaxies in dense environments exceeds that in less dense regions, likely due to the greater availability of cold gas, higher merger rates, and tidal effects that trigger star formation activity.

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arXiv2024

UVCANDELS: Catalogs of photometric redshifts and galaxy physical properties

The UltraViolet imaging of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey Fields (UVCANDELS) program provides deep HST F275W and F435W imaging over four CANDELS fields (GOODS-N, GOODS-S, COSMOS, and EGS). We combine this newly acquired UV imaging with existing HST imaging from CANDELS as well as existing ancillary data to obtain robust photometric redshifts and reliable estimates for galaxy physical properties for over 150,000 galaxies in the $\sim$430 arcmin$^2$ UVCANDELS area. Here, we leverage the power of the new UV photometry to not only improve the photometric redshift measurements in these fields, but also constrain the full redshift probability distribution combining multiple redshift fitting tools. Furthermore, using the full UV-to-IR photometric dataset, we measure the galaxy physical properties by fitting templates from population synthesis models with two different parameterizations (flexible and fixed-form) of the star-formation histories (SFHs). Compared to the flexible SFH parametrization, we find that the fixed-form SFHs systematically underestimate the galaxy stellar masses, both at the low- ($\lesssim10^9 M_\odot$) and high- ($\gtrsim10^{10} M_\odot$) mass end, by as much as $\sim0.5$ dex. This underestimation is primarily due the limited ability of fixed-form SFH parameterization to simultaneously capture the chaotic nature of star-formation in these galaxies.

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arXiv2024

Dynamics of Star-forming Galaxies in a Massive Structure at \lowercase{$z\sim$} 2.2: Evidence for Galaxy Harassment in high-$z$ Environments

We spectroscopically confirm a new protocluster in the COSMOS field at $z$=2.24430 with Keck/MOSFIRE, dubbed CC2.2B, which is in the immediate vicinity of CC2.2A protocluster, originally presented in \cite{Darvish20}. CC2.2B and CC2.2A centroids are separated by $\sim$5.5 Mpc(angular) and $\sim$16 comoving Mpc(radial). CC2.2B and CC2.2A have similar properties, with CC2.2B having a line-of-sight velocity dispersion and estimated total mass of $σ_{los}$=693$\pm$65 km s$^{-1}$ and $M_{total}$=($\sim$2-3)$\times$10$^{14}$ $M_{\odot}$, respectively. These two similar overdensities are likely still in the merging process and will likely collapse into a more massive structure at lower redshifts. We combine CC2.2A and CC2.2B data to investigate the role of high-$z$ protocluster environments on the dynamics of star-forming (SF) galaxies compared to a similarly selected field sample. We find that on average, protocluster SF galaxies have $\sim$0.1 dex (at $\sim$1.8$σ$ significance) lower gas velocity dispersions, $\sim$0.2 dex (at $\sim$2.2$σ$ significance) lower dynamical masses, and $\sim$0.2 dex lower dynamical-to-stellar mass ratio than the field SF galaxies. We argue that galaxy harassment and galaxy-galaxy interactions can potentially explain these differences. We also find a factor of $\sim$2-3 lower scatter around the mean $σ$-$M_{*}$, $M_{dyn}$-$M_{*}$, and $M_{dyn}$/$M_{*}$ vs. $M_{*}$ relations for protocluster SF galaxies than the field. This could be due to a more uniform formation for protocluster galaxies than their field counterparts. Our results have potential implications for the physics of preprocessing in early environments.

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arXiv2024

UVCANDELS: The role of dust on the stellar mass-size relation of disk galaxies at 0.5 $\leq z \leq$ 3.0

We use the Ultraviolet Imaging of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey fields (UVCANDELS) to measure half-light radii in the rest-frame far-UV for $\sim$16,000 disk-like galaxies over $0.5\leq z \leq 3$. We compare these results to rest-frame optical sizes that we measure in a self-consistent way and find that the stellar mass-size relation of disk galaxies is steeper in the rest-frame UV than in the optical across our entire redshift range. We show that this is mainly driven by massive galaxies ($\gtrsim10^{10}$M$_\odot$), which we find to also be among the most dusty. Our results are consistent with the literature and have commonly been interpreted as evidence of inside-out growth wherein galaxies form their central structures first. However, they could also suggest that the centers of massive galaxies are more heavily attenuated than their outskirts. We distinguish between these scenarios by modeling and selecting galaxies at $z=2$ from the VELA simulation suite in a way that is consistent with UVCANDELS. We show that the effects of dust alone can account for the size differences we measure at $z=2$. This indicates that, at different wavelengths, size differences and the different slopes of the stellar mass-size relation do not constitute evidence for inside-out growth.

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arXiv2024

The UV luminosity function at 0.6 < z < 1 from UVCANDELS

UVCANDELS is a HST Cycle-26 Treasury Program awarded 164 orbits of primary ultraviolet (UV) F275W imaging and coordinated parallel optical F435W imaging in four CANDELS fields: GOODS-N, GOODS-S, EGS, and COSMOS, covering a total area of $\sim426$ arcmin$^2$. This is $\sim2.7$ times larger than the area covered by previous deep-field space UV data combined, reaching a depth of about 27 and 28 ABmag ($5σ$ in $0.2"$ apertures) for F275W and F435W, respectively. Along with the new photometric catalogs, we present an analysis of the rest-frame UV luminosity function (LF), relying on our UV-optimized aperture photometry method yielding a factor of $1.5\times$ increase than the H-isophot aperture photometry in the signal-to-noise ratios of galaxies in our F275W imaging. Using well tested photometric redshift measurements we identify 5810 galaxies at redshifts $0.6<z<1$, down to an absolute magnitude of $M_\text{UV} = -14.2$. In order to minimize the effect of uncertainties in estimating the completeness function, especially at the faint-end, we restrict our analysis to sources above $30\%$ completeness, which provides a final sample of 4726 galaxies at $-21.5<M_\text{UV}<-15.5$. We performed a maximum likelihood estimate to derive the best-fit parameters of the UV LF. We report a best-fit faint-end slope of $α= -1.359^{+0.041}_{-0.041}$ at $z \sim 0.8$. Creating sub-samples at $z\sim0.7$ and $z\sim0.9$, we observe a possible evolution of $α$ with redshift. The unobscured UV luminosity density at $M_\text{UV}<-10$ is derived as $ρ_\text{UV}=1.339^{+0.027}_{-0.030}\ (\times10^{26} \text{ergs/s/Hz/Mpc}^3)$ using our best-fit LF parameters. The new F275W and F435 photometric catalogs from UVCANDELS have been made publicly available on the Barbara A. Mikulski Archive for Space Telescopes (MAST).

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arXiv2022

Structure of cosmic web in non-linear regime: the nearest neighbour and spherical contact distributions

In non-linear scales, the matter density distribution is not Gaussian. Consequently, the widely used two-point correlation function is not adequate anymore to capture the matter density field's entire behaviour. Among all statistics beyond correlation functions, the spherical contact (or equivalently void function), and nearest neighbour distribution function seem promising tools to probe matter distribution in non-linear regime. In this work, we use halos from cosmological N-body simulations, galaxy groups from the volume-limited galaxy group and central galaxies from mock galaxy catalogues, to compare the spherical contact with the nearest neighbour distribution functions. We also calculate the J-function (or equivalently the first conditional correlation function), for different samples. Moreover, we consider the redshift evolution and mass-scale dependence of statistics in the simulations and dependence on the magnitude of volume-limited samples in group catalogues as well as the mock central galaxies. The shape of the spherical contact probability distribution function is nearly skew-normal, with skewness and kurtosis being approximately 0.5 and 3, respectively. On the other hand, the nearest neighbour probability distribution function is nearly log-normal, with logarithmic skewness and kurtosis being approximately 0.1 and 2.5, respectively. Accordingly, the spherical contact distribution function probes larger scales compared to the nearest neighbour distribution function, which is influenced by details of structures. We also find a linear relation between the mean and variance of the spherical contact probability distribution function in simulations and mock galaxies, which could be used as a distinguishing probe of cosmological models.

astro-ph.CO↗
arXiv2019

Cosmological Filaments in the light of Excursion Set of Saddle Points

The universe in large scales is structured as a network known as cosmic web. Filaments are one of the structural components of this web, which can be introduced as a novel probe to study the formation and evolution of structures and as a probe to study the cosmological models and to address the missing baryon problem. The aim of this work is to introduce an analytical framework to study the statistics of filaments such as number density of them and also to obtain the length-mass relation. For this objective, we model filaments as collapsed objects which have an extension in one direction, accordingly we use the ellipsoidal collapse to study the evolution of an over-dense region via gravitational instability. %In this context, we consider the critical density of filament formation, which will be a crucial parameter for number density count. We find that the nonlinear density of filaments in the epoch of formation is almost mass independent and is in order of $\sim 30$. By introducing {\it{filament's extended condition}} we find a fitting function for length-mass relation. For the statistics of filaments, we propose a novel framework named excursion set of saddle points. In this approach, we count the saddle points of the density field Hessian matrix, and relate it to the count of filaments. In addition, we addressed the filament in filament problem with up-crossing approximation.

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