arXiv subjects

Harinder P. Singh

Publications and source records attributed to Harinder P. Singh.

At least 37 records · Page 2Linked to original sources

arXiv2020

A study of the stellar photosphere-hydrogen ionisation front interaction in pulsating variables using period-color relations

Period-color (PC) relations may be used to study the interaction of the stellar photosphere and the hydrogen ionization front (HIF). RR Lyraes (RRLs) and long period classical Cepheids (P > 10d) have been found to exhibit different PC behavior at minimum and maximum light which can be explained by the HIF-photosphere interaction based on their location on the HR diagram. In this work, we extend the study to include type II Cepheids (T2Cs) with an aim to test the HIF-photosphere interaction theory across a broad spectrum of variable star types. We find W Vir stars and BL Her stars to have similar PC relations as those from long period and short period classical Cepheids, respectively. We also use MESA to compute RRL, BL Her and classical Cepheid models to study the theoretical HIF-photosphere distance and find the results to be fairly consistent with the HIF-photosphere interaction theory.

astro-ph.SR↗

arXiv2020

Near-infrared Census of RR Lyrae variables in the Messier 3 globular cluster and the Period--Luminosity Relations

We present new near-infrared ($JHK_s$) time-series observations of RR Lyrae variables in the Messier 3 (NGC 5272) globular cluster using the WIRCam instrument at the 3.6-m Canada France Hawaii Telescope. Our observations cover a sky area of $\sim 21'\times 21'$ around the cluster center and provide an average of twenty epochs of homogeneous $JHK_s$-band photometry. New homogeneous photometry is used to estimate robust mean magnitudes for 175 fundamental-mode (RRab), 47 overtone-mode (RRc), and 11 mixed-mode (RRd) variables. Our sample of 233 RR Lyrae variables is the largest thus far obtained in a single cluster with time-resolved, multi-band near-infrared photometry. Near-infrared to optical amplitude ratios for RR Lyrae in Messier 3 exhibit a systematic increase moving from RRc to short-period ($P < 0.6$~days) and long-period ($P \gtrsim 0.6$~days) RRab variables. We derive $JHK_s$-band Period--Luminosity relations for RRab, RRc, and the combined sample of variables. Absolute calibrations based on the theoretically predicted Period--Luminosity--Metallicity relations for RR Lyrae stars yield a distance modulus, $μ= 15.041 \pm 0.017~(\textrm{statistical}) \pm 0.036~(\textrm{systematic})$~mag, to Messier 3. When anchored to trigonometric parallaxes for nearby RR Lyrae stars from the {\it Hubble Space Telescope} and the {\it Gaia} mission, our distance estimates are consistent with those resulting from the theoretical calibrations, albeit with relatively larger systematic uncertainties.

astro-ph.SR↗

arXiv2020

Stellar Spectral Interpolation using Machine Learning

Theoretical stellar spectra rely on model stellar atmospheres computed based on our understanding of the physical laws at play in the stellar interiors. These models, coupled with atomic and molecular line databases, are used to generate theoretical stellar spectral libraries (SSLs) comprising of stellar spectra over a regular grid of atmospheric parameters (temperature, surface gravity, abundances) at any desired resolution. Another class of SSLs is referred to as empirical spectral libraries; these contain observed spectra at limited resolution. SSLs play an essential role in deriving the properties of stars and stellar populations. Both theoretical and empirical libraries suffer from limited coverage over the parameter space. This limitation is overcome to some extent by generating spectra for specific sets of atmospheric parameters by interpolating within the grid of available parameter space. In this work, we present a method for spectral interpolation in the optical region using machine learning algorithms that are generic, easily adaptable for any SSL without much change in the model parameters, and computationally inexpensive. We use two machine learning techniques, Random Forest (RF) and Artificial Neural Networks (ANN), and train the models on the MILES library. We apply the trained models to spectra from the CFLIB for testing and show that the performance of the two models is comparable. We show that both the models achieve better accuracy than the existing methods of polynomial based interpolation and the Gaussian radial basis function (RBF) interpolation.

astro-ph.SR↗

arXiv2020

The stellar photosphere-hydrogen ionization front interaction in Classical Pulsators: a theoretical explanation for observed period-colour relations

Period-colour and amplitude-colour (PCAC) relations can be used to probe both the hydrodynamics of outer envelope structure and evolutionary status of Cepheids and RR Lyraes. In this work, we incorporate the PCAC relations for RR Lyraes, BL Her, W Vir and classical Cepheids in a single unifying theory that involves the interaction of the hydrogen ionization front (HIF) and stellar photosphere and the theory of stellar evolution. PC relations for RR Lyraes and classical Cepheids using OGLE-IV data are found to be consistent with this theory: RR Lyraes have shallow/sloped relations at minimum/maximum light whilst long-period ($P>10$ days) Cepheids exhibit sloped/flat PC relations at minimum/maximum light. The differences in the PC relations for Cepheids and RR Lyraes can be explained based on the relative location of the HIF and stellar photosphere which changes depending on their position on the HR diagram. We also extend our analysis of PCAC relations for type II Cepheids in the Galactic bulge, LMC and SMC using OGLE-IV data. We find that BL Her stars have sloped PC relations at maximum and minimum light similar to short-period ($P<10$ days) classical Cepheids. W Vir stars exhibit sloped/flat PC relation at minimum/maximum light similar to long-period classical Cepheids. We also compute state-of-the-art 1D radiation hydrodynamic models of RR Lyraes, BL Her and classical Cepheids using the radial stellar pulsation code in MESA to further test these ideas theoretically and find that the models are generally consistent with this picture. We are thus able to explain PC relations at maximum and minimum light across a broad spectrum of variable star types.

astro-ph.SR↗

arXiv2020

Unveiling Vela -- Variability of Interstellar Lines in the Direction of the Vela Supernova Remnant III. Na D and Ca II K

High-resolution optical spectra were obtained in 2017-2019 with The Southern African Large Telescope of fifteen stars in the direction of the Vela supernova remnant. Interstellar Ca ii H and K and Na i D lines are discussed in this paper. In particular, the line profiles are compared with profiles at a comparable spectral resolution obtained in 1993-1996 by Cha & Sembach. Ten of the lines of sight show changes to one or more of the components in that line of sight. Changes include small changes (1-2 km/s) in radial velocity and/or increases/decreases in equivalent width over the two decades between the periods of observation. Changes are more obvious in the Ca K line than in the Na D lines. These changes are attributed to gas disturbed by interactions between the supernova ejecta and the surrounding interstellar medium. A representative timescale may be 20-50 years. Small-scale variations in line profiles across the face of the remnant suggest, as previously remarked, that a linear scale for interactions is a small fraction of the 40 pc size of the present remnant.

astro-ph.SR↗

arXiv2019

The Tale of the Milky Way Globular Cluster NGC 6362 -- I. The Orbit and its possible extended star debris features as revealed by Gaia DR2

We report the identification of possible extended star debris candidates beyond the cluster tidal radius of NGC 6362 based on the second {\it Gaia} data release ({\it Gaia} DR2). We found 259 objects possibly associated with the cluster lying in the vicinity of the giant branch and 1--2 magnitudes fainter/brighter than the main-sequence turn-off in the cluster color-magnitude diagram and which cover an area on the sky of $\sim$4.1 deg$^{2}$ centered on the cluster. We traced back the orbit of NGC 6362 in a realistic Milky-Way potential, using the \texttt{GravPot16} package, for 3 Gyrs. The orbit shows that the cluster shares similar orbital properties as the inner disk, having peri-/apo-galactic distances, and maximum vertical excursion from the Galactic plane inside the corotation radius (CR), moving inwards from CR radius to visit the inner regions of the Milky Way. The dynamical history of the cluster reveals that it has crossed the Galactic disk several times in its lifetime and has recently undergone a gravitational shock, $\sim 15.9$ Myr ago, suggesting that less than 0.1\% of its mass has been lost during the current disk-shocking event. Based on the cluster's orbit and position in the Galaxy, we conclude that the possible extended star debris candidates are a combined effect of the shocks from the Galactic disk and evaporation from the cluster. Lastly, the evolution of the vertical component of the angular momentum shows that the cluster is strongly affected dynamically by the Galactic bar potential.

astro-ph.GA↗

arXiv2019

Multiwavelength Period-Luminosity and Period-Luminosity-Color relations at maximum-light for Mira variables in the Magellanic Clouds

We present Period-Luminosity and Period-Luminosity-Color relations at maximum-light for Mira variables in the Magellanic Clouds using time-series data from the Optical Gravitational Lensing Experiment (OGLE-III) and {\it Gaia} data release 2. The maximum-light relations exhibit a scatter typically up to $\sim 30\%$ smaller than their mean-light counterparts. The apparent magnitudes of Oxygen-rich Miras at maximum-light display significantly smaller cycle-to-cycle variations than at minimum-light. High-precision photometric data for Kepler Mira candidates also exhibit stable magnitude variations at the brightest epochs while their multi-epoch spectra display strong Balmer emission lines and weak molecular absorption at maximum-light. The stability of maximum-light magnitudes for Miras possibly occurs due to the decrease in the sensitivity to molecular bands at their warmest phase. At near-infrared wavelengths, the Period-Luminosity relations of Miras display similar dispersion at mean and maximum-light with limited time-series data in the Magellanic Clouds. A kink in the Oxygen-rich Mira Period-Luminosity relations is found at 300 days in the $VI$-bands which shifts to longer-periods ($\sim 350$~days) at near-infrared wavelengths. Oxygen-rich Mira Period-Luminosity relations at maximum-light provide a relative distance modulus, $Δμ= 0.48\pm0.08$~mag, between the Magellanic Clouds with a smaller statistical uncertainty than the mean-light relations. The maximum-light properties of Miras can be very useful for stellar atmosphere modeling and distance scale studies provided their stability and the universality can be established in other stellar environments in the era of extremely large telescopes.

astro-ph.SR↗

arXiv2019

Light Curve Parameters of Cepheid and RR Lyrae Variables at Multiple Wavelengths $-$ Models vs. Observations

We present results from a comparative study of light curves of Cepheid and RR Lyrae stars in the Galaxy and the Magellanic Clouds with their theoretical models generated from the stellar pulsation codes. Fourier decomposition method is used to analyse the theoretical and the observed light curves at multiple wavelengths. In case of RR Lyrae stars, the amplitude and Fourier parameters from the models are consistent with observations in most period bins except for low metal-abundances ($Z<0.004$). In case of Cepheid variables, we observe a greater offset between models and observations for both the amplitude and Fourier parameters. The theoretical amplitude parameters are typically larger than those from observations, except close to the period of $10$ days. We find that these discrepancies between models and observations can be reduced if a higher convective efficiency is adopted in the pulsation codes. Our results suggest that a quantitative comparison of light curve structure is very useful to provide constraints for the input physics to the stellar pulsation models.

astro-ph.SR↗

arXiv2018

Search for Extra-Tidal RR Lyrae Stars in Milky Way Globular Clusters From Gaia DR2

We used extra-tidal RR Lyrae stars to study the dynamics of Galactic globular clusters and know how effects like dynamical friction and tidal disruption affect these clusters. The Gaia DR2 catalog for RR Lyrae stars (Clementini et al. 2018) is used along with the proper motions and tidal radii data for the globular clusters compiled from literature. A sample of 56 Galactic globular clusters is analyzed. Out of these 56 Galactic globular clusters, only 11 have extra-tidal RR Lyrae stars. However, only two clusters, namely, NGC 3201 and NGC 5024, have enough extra-tidal RR Lyrae stars to draw interesting conclusions. NGC 3201 has 13 extra-tidal RR Lyrae stars which are asymmetrically distributed around its center with more number of stars in its trailing zone than its leading part. We conclude that these asymmetrical tidal tails are due to the combined effect of tidal disruption and the stripped debris from the cluster. On the other hand, NGC 5024 has 5 extra-tidal RR Lyrae stars, four of them are concentrated in a region which is at a distance of about 3 times the tidal radius from its center. These may be the stars that are being ripped apart from the cluster due to tidal disruption. The presence of these extra-tidal RR Lyrae stars in the clusters can be an indication that more cluster stars are present outside their tidal radii which may be revealed by deep wide field CMDs of the clusters.

astro-ph.GA↗

arXiv2018

On the variation of light curve parameters of RR Lyrae variables at multiple wavelengths

We present a detailed light curve analysis of RR Lyrae variables at multiple wavelengths using Fourier decomposition method. The time-series data for RR Lyrae variables in the Galactic bulge and the Magellanic Clouds are taken from the Optical Gravitational Lensing Experiment survey while the infrared light curves are compiled from the literature. We also analyse the multiband theoretical light curves that are generated from the stellar pulsation models of RR Lyrae stars for a wide range of metal-abundances. We find that the theoretical light curve parameters with different metal abundances are consistent with observed parameters in most period bins at both optical and infrared wavelengths. The theoretical and observed Fourier amplitude parameters decrease with increase in wavelength while the Fourier phase parameters increase with wavelength at a given period. We use absolute magnitudes for a subset of theoretical models that fit the observed optical RR Lyrae light curves in the Large Magellanic Cloud to estimate a distance modulus, $μ_\textrm{LMC}=18.51\pm0.07$, independent of the metallicity. We also use Fourier analysis to study the period-color and amplitude-color relations for RR Lyrae stars in the Magellanic Clouds using optical data and find that the slope of period-color relation at minimum light is very shallow or flat and becomes increasingly significant at the maximum light for RRab stars. We also find that the metallicity dependence of the period-color relations increases as we go from minimum to maximum light, suggesting that the mean light results are indeed an average of the various pulsational phases. We summarize that the average variation in these relations is consistent between theory and observations and supports the theory of the interaction of the stellar photosphere and the hydrogen ionization front.

astro-ph.SR↗

arXiv2018

Geometry of the Large Magellanic Cloud Using Multi- wavelength Photometry of Classical Cepheids

We determine the geometrical and viewing angle parameters of the Large Magellanic Cloud (LMC) using the Leavitt law based on a sample of more than $3500$ common classical Cepheids (FU and FO) in optical ($V,I$), near-infrared ($JHK_{s}$) and mid-infrared ($[3.6]~μ$m and $[4.5]~μ$m) photometric bands. Statistical reddening and distance modulus free from the effect of reddening to each of the individual Cepheids are obtained using the simultaneous multi-band fit to the apparent distance moduli from the analysis of the resulting Leavitt laws in these seven photometric bands. A reddening map of the LMC obtained from the analysis shows good agreement with the other maps available in the literature. Extinction free distance measurements along with the information of the equatorial coordinates $(α,δ)$ for individual stars are used to obtain the corresponding Cartesian coordinates with respect to the plane of the sky. By fitting a plane solution of the form $z=f(x,y)$ to the observed three dimensional distribution, the following viewing angle parameters of the LMC are obtained: inclination angle $i=25^{\circ}.110\pm 0^{\circ}.365$, position angle of line of nodes $θ_{\text{lon}}=154^{\circ}.702\pm1^{\circ}.378$. On the other hand, modelling the observed three dimensional distribution of the Cepheids as a triaxial ellipsoid, the following values of the geometrical axes ratios of the LMC are obtained: $1.000\pm 0.003:1.151\pm0.003:1.890\pm 0.014$ with the viewing angle parameters: inclination angle of $i=11^{\circ}.920\pm 0^{\circ}.315$ with respect to the longest axis from the line of sight and position angle of line of nodes $θ_{\rm lon} = 128^{\circ}.871\pm 0^{\circ}.569$. The position angles are measured eastwards from north.

astro-ph.GA↗

arXiv2017

Growth of bulges in disc galaxies since $z\sim1$

We investigate the growth of bulges in bright ($M_B<-20$) disc galaxies since $z\sim1$, in rest-frame B and I-band, using images from HST ACS and WFC3 in GOODS-South for high redshifts ($0.4<z<1.0$) and SDSS for local ($0.02<z<0.05$). The growth history has been traced by performing two-component bulge-disc decomposition and further classifying the bulges into pseudos and classicals using Kormendy relation. We have about $27\%$ pseudo and $40\%$ classical bulges in our sample. Classical bulges are brighter than pseudo, in both rest-bands, at all redshifts probed here; in fact since $z\sim0.77$, classical are about $\sim1$ mag brighter than pseudo bulges. Both bulges have witnessed substantial growth, more than half of their present day stellar mass has been gained since $z\sim1$. Their host discs have grown concurrently, becoming progressively brighter in rest-frame I-band. The high redshift host discs of both pseudo and classical bulges are found to be equally clumpy in rest-frame B-band. In the same band, we found that the growth of classical bulges is accompanied by fading of their host discs - which might be an indication of secular processes in action. However, both host disc as well as the bulge have grown substantially in terms of stellar mass. Our analysis suggests that, clump migration and secular processes alone can not account for the bulge growth, since $z\sim1$, accretion and minor mergers would be required.

astro-ph.GA↗

arXiv2017

Multiwavelength Light Curve Parameters of Cepheid Variables

We present a comparative analysis of theoretical and observed light curves of Cepheid variables using Fourier decomposition. The theoretical light curves at multiple wavelengths are generated using stellar pulsation models for chemical compositions representative of Cepheids in the Galaxy and Magellanic Clouds. The observed light curves at optical ({\it VI}), near-infrared ({\it JHK}$_s$) and mid-infrared (3.6 $\&$ 4.5-$μ$m) bands are compiled from the literature. We discuss the variation of light curve parameters as a function of period, wavelength and metallicity. Theoretical and observed Fourier amplitude parameters decrease with increase in wavelength while the phase parameters increase with wavelength. We find that theoretical amplitude parameters obtained using canonical mass-luminosity levels exhibit a greater offset with respect to observations when compared to non-canonical relations. We also discuss the impact of variation in convective efficiency on the light curve structure of Cepheid variables. The increase in mixing length parameter results in a zero-point offset in bolometric mean magnitudes and reduces the systematic large difference in theoretical amplitudes with respect to observations.

astro-ph.SR↗

arXiv2017

Large Magellanic Cloud Near-Infrared Synoptic Survey. IV. Leavitt Laws for Type II Cepheid Variables

We present time-series observations of Population \rom{2} Cepheids in the Large Magellanic Cloud at near-infrared ($JHK_s$) wavelengths. Our sample consists of 81 variables with accurate periods and optical ($VI$) magnitudes from the OGLE survey, covering various subtypes of pulsators (BL Herculis, W Virginis and RV Tauri). We generate light curve templates using high-quality $I$-band data in the LMC from OGLE and $K_s$-band data in the Galactic Bulge from VVV and use them to obtain robust mean magnitudes. We derive Period-Luminosity (P-L) relations in the near-infrared and Period-Wesenheit (P-W) relations by combining optical and near-infrared data. Our P-L and P-W relations are consistent with published work when excluding long-period RV Tauris. We find that Pop II Cepheids and RR Lyraes follow the same P-L relations in the LMC. Therefore, we use trigonometric parallax from the {\it Gaia DR1} for VY~Pyx and the {\it Hubble Space Telescope} parallaxes for $k$~Pav and 5 RR Lyrae variables to obtain an absolute calibration of the Galactic $K_s$-band P-L relation, resulting in a distance modulus to the LMC of $μ_{\rm LMC} = 18.54\pm0.08$~mag. We update the mean magnitudes of Pop~II Cepheids in Galactic globular clusters using our light curve templates and obtain distance estimates to those systems, anchored to a precise late-type eclipsing binary distance to the LMC. We find the distances to these globular clusters based on Pop~II Cepheids are consistent (within $2σ$) with estimates based on the $M_V-[\rm{Fe}/\rm{H}]$ relation for horizontal branch stars.

astro-ph.SR↗

arXiv2017

Unveiling Vela - Time Variability of Interstellar Lines in the Direction of the Vela Supernova Remnant II. Na D and Ca II

In a survey conducted between 2011-12 of interstellar Na I D line profiles in the direction of the Vela supernova remnant, a few lines of sight showed dramatic changes in low velocity absorption components with respect to profiles from 1993-1994 reported by Cha & Sembach. Three stars - HD 63578, HD 68217 and HD 76161 showed large decrease in strength over the 1993-2012 interval. HD 68217 and HD 76161 are associated with the Vela SNR whereas HD 63578 is associated with $γ^2$ Velorum wind bubble. Here, we present high spectral resolution observations of Ca II K lines obtained with the Southern African Large Telescope (SALT) towards these three stars along with simultaneous observations of Na I D lines. These new spectra confirm that the Na D interstellar absorption weakened drastically between 1993-1994 and 2011-2012 but show for the first time that the Ca II K line is unchanged between 1993-1994 and 2015. This remarkable contrast between the behaviour of Na D and Ca II K line absorption lines is a puzzle concerning gas presumably affected by the outflow from the SNR and the wind from $γ^2$ Velorum.

astro-ph.SR↗

arXiv2017

High-resolution Spectroscopy and Spectropolarimetry of Selected Delta Scuti Pulsating Variables

The combination of photometry, spectroscopy and spectropolarimetry of the chemically peculiar stars often aims to study the complex physical phenomena such as stellar pulsation, chemical inhomogeneity, magnetic field and their interplay with stellar atmosphere and circumstellar environment. The prime objective of the present study is to determine the atmospheric parameters of a set of Am stars to understand their evolutionary status. Atmospheric abundances and basic parameters are determined using full spectrum fitting technique by comparing the high-resolution spectra to the synthetic spectra. To know the evolutionary status we derive the effective temperature and luminosity from different methods and compare them with the literature. The location of these stars in the H-R diagram demonstrate that all the sample stars are evolved from the Zero-Age-Main-Sequence towards Terminal-Age-Main-Sequence and occupy the region of $δ$ Sct instability strip. The abundance analysis shows that the light elements e.g. Ca and Sc are underabundant while iron peak elements such as Ba, Ce etc. are overabundant and these chemical properties are typical for Am stars. The results obtained from the spectropolarimetric analysis shows that the longitudinal magnetic fields in all the studied stars are negligible that gives further support their Am class of peculiarity.

astro-ph.SR↗

arXiv2016

A Comparative Study of Multiwavelength Theoretical and Observed Light Curves of Cepheid Variables

We analyse the theoretical light curves of Cepheid variables at optical ({\it UBVRI}) and near-infrared ({\it JKL}) wavelengths using the Fourier decomposition and principal component analysis methods. The Cepheid light curves are based on the full amplitude, nonlinear, convective hydrodynamical models for chemical compositions representative of Cepheids in the Galaxy ($Y=0.28$, $Z=0.02$), Large Magellanic Cloud ($Y=0.25$, $Z=0.008$) and Small Magellanic Cloud ($Y=0.25$, $Z=0.004$). We discuss the variation of light curve parameters with different compositions and mass-luminosity levels as a function of period and wavelength, and compare our results with observations. For a fixed composition, the theoretical amplitude parameters decrease while the phase parameters increase with wavelength, similar to the observed Fourier parameters. The optical amplitude parameters obtained using canonical mass-luminosity Cepheid models, exhibit a large offset with respect to the observations for periods between 7-11 days, when compared to the non-canonical mass-luminosity levels. The central minimum of the Hertzsprung progression for amplitude parameters, shifts to the longer periods with decrease/increase in metallicity/wavelength for both theoretical and observed light curves. The principal components for Magellanic Clouds Cepheid models are consistent with observations at optical wavelengths. We also observe two distinct populations in the first principal component for optical and near-infrared wavelengths while $J$-band contributes to both populations. Finally, we take into account the variation in the convective efficiency by increasing the adopted mixing length parameter from the standard 1.5 to 1.8. This results in a zero-point offset in the bolometric mean magnitudes and in amplitude parameters (except close to 10 days), reducing the systematically large difference in theoretical amplitudes.

astro-ph.GA↗

arXiv2016

Period-Color and Amplitude-Color Relations at Maximum and Minimum Light for RR Lyrae Stars in the SDSS Stripe 82 Region

Investigation of period-color (PC) and amplitude-color (AC) relations at the maximum and minimum light can be used to probe the interaction of the hydrogen ionization front (HIF) with photosphere and the radiation hydrodynamics of the outer envelopes of Cepheids and RR Lyraes. For example, theoretical calculations indicated that such interactions would occur at minimum light for RR Lyrae and result in a flatter PC relation. In the past, the PC and AC relations have been investigated by using either the $(V-R)_{MACHO}$ or $(V-I)$ colors. In this work, we extend previous work to other bands by analyzing the RR Lyraes in the Sloan Digital Sky Survey Stripe 82 Region. Multi-epoch data is available for RR Lyraes located within the footprint of the Stripe 82 Region in five ($ugriz$) bands. We present the PC and AC relations at maximum and minimum light in four colors: $(u-g)_0$, $(g-r)_0$, $(r-i)_0$ and $(i-z)_0$, after they are corrected for extinction. We found that the PC and AC relations for this sample of RR Lyraes show a complex nature in the form of flat, linear or quadratic relations. Furthermore, the PC relations at minimum light for fundamental mode RR Lyrae stars are separated according to the Oosterhoff type, especially in the $(g-r)_0$ and $(r-i)_0$ colors. If only considering the results from linear regressions, our results are quantitatively consistent with the theory of HIF-photosphere interaction for both fundamental and first overtone RR Lyraes.

astro-ph.SR↗