arXiv subjects

G. Bono

Publications and source records attributed to G. Bono.

At least 73 records · Page 4Linked to original sources

arXiv2016

Astrometry with MCAO: HST-GeMS proper motions in the globular cluster NGC 6681

Aims: for the first time the astrometric capabilities of the Multi-Conjugate Adaptive Optics (MCAO) facility GeMS with the GSAOI camera on Gemini-South are tested to quantify the accuracy in determining stellar proper motions in the Galactic globular cluster NGC 6681. Methods: proper motions from HST/ACS for a sample of its stars are already available, and this allows us to construct a distortion-free reference at the epoch of GeMS observations that is used to measure and correct the temporally changing distortions for each GeMS exposure. In this way, we are able to compare the corrected GeMS images with a first-epoch of HST/ACS images to recover the relative proper motion of the Sagittarius dwarf spheroidal galaxy with respect to NGC 6681. Results: we find this to be (μ_αcosδ, μ_δ) = (4.09,-3.41) mas/yr, which matches previous HST/ACS measurements with a very good accuracy of 0.03 mas/yr and with a comparable precision (r.m.s of 0.43 mas/yr). Conclusions: this study successfully demonstrates that high-quality proper motions can be measured for quite large fields of view (85 arcsec X 85 arcsec) with MCAO-assisted, ground-based cameras and provides a first, successful test of the performances of GeMS on multi-epoch data.

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arXiv2016

On the RR Lyrae stars in globulars: IV. $ω$ Centauri Optical UBVRI Photometry

New accurate and homogeneous optical UBVRI photometry has been obtained for variable stars in the Galactic globular $ω$ Cen (NGC 5139). We secured 8202 CCD images covering a time interval of 24 years and a sky area of 84x48 arcmin. The current data were complemented with data available in the literature and provided new, homogeneous pulsation parameters (mean magnitudes, luminosity amplitudes,periods) for 187 candidate $ω$ Cen RR Lyrae (RRLs). Among them we have 101 RRc (first overtone), 85 RRab (fundamental) and a single candidate RRd (double-mode) variables. Candidate Blazhko RRLs show periods and colors that are intermediate between RRc and RRab variables, suggesting that they are transitional objects. The comparison of the period distribution and of the Bailey diagram indicates that RRLs in $ω$ Cen show a long-period tail not present in typical Oosterhoff II (OoII) globulars. The RRLs in dwarf spheroidals and in ultra faint dwarfs have properties between Oosterhoff intermediate and OoII clusters. Metallicity plays a key role in shaping the above evidence. These findings do not support the hypothesis that $ω$ Cen is the core remnant of a spoiled dwarf galaxy. Using optical Period-Wesenheit relations that are reddening-free and minimally dependent on metallicity we find a mean distance to $ω$ Cen of 13.71$\pm$0.08$\pm$0.01 mag (semi-empirical and theoretical calibrations). Finally, we invert the I-band Period-Luminosity-Metallicity relation to estimate individual RRLs metal abundances. The metallicity distribution agrees quite well with spectroscopic and photometric metallicity estimates available in the literature.

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arXiv2016

The panchromatic view of the Magellanic Clouds from Classical Cepheids. I. Distance, Reddening and Geometry of the Large Magellanic Cloud disk

We present a detailed investigation of the Large Magellanic Cloud (LMC) disk using classical Cepheids. Our analysis is based on optical (I,V; OGLE-IV), near-infrared (NIR: J,H,Ks) and mid-infrared (MIR: w1; WISE) mean magnitudes. By adopting new templates to estimate the NIR mean magnitudes from single-epoch measurements, we build the currently most accurate, largest and homogeneous multi-band dataset of LMC Cepheids. We determine Cepheid individual distances using optical and NIR Period-Wesenheit relations (PWRs), to measure the geometry of the LMC disk and its viewing angles. Cepheid distances based on optical PWRs are precise at 3%, but accurate to 7, while the ones based on NIR PWRs are more accurate (to 3%), but less precise (2%-15%), given the higher photometric error on the observed magnitudes. We found an inclination i=25.05 $\pm$ 0.02 (stat.) $\pm$ 0.55 (syst.) deg, and a position angle of the lines of nodes P.A.=150.76 $\pm$ 0.02(stat.) $\pm$ 0.07(syst.) deg. These values agree well with estimates based either on young (Red Supergiants) or on intermediate-age (Asymptotic Giant Branch, Red Clump) stellar tracers, but they significantly differ from evaluations based on old (RR Lyrae) stellar tracers. This indicates that young/intermediate and old stellar populations have different spatial distributions. Finally, by using the reddening-law fitting approach, we provide a reddening map of the LMC disk which is ten times more accurate and two times larger than similar maps in the literature. We also found an LMC true distance modulus of $μ_{0,LMC}=18.48 \pm 0.10$ (stat. and syst.) mag, in excellent agreement with the currently most accurate measurement (Pietrzynski et al. 2013).

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arXiv2016

Variable stars in Local Group Galaxies - II. Sculptor dSph

We present the identification of 634 variable stars in the Milky Way dSph satellite Sculptor based on archival ground-based optical observations spanning $\sim$24 years and covering $\sim$ 2.5 deg$^2$. We employed the same methodologies as the "Homogeneous Photometry" series published by Stetson. In particular, we have identified and characterized one of the largest (536) RR Lyrae samples so far in a Milky Way dSph satellite. We have also detected four Anomalous Cepheids, 23 SX Phoenicis stars, five eclipsing binaries, three field variable stars, three peculiar variable stars located above the horizontal branch - near to the locus of BL Herculis - that we are unable to classify properly. Additionally we identify 37 Long Period Variables plus 23 probable variable stars, for which the current data do not allow us to determine the period. We report positions and finding charts for all the variable stars, and basic properties (period, amplitude, mean magnitude) and light curves for 574 of them. We discuss the properties of the RR Lyrae stars in the Bailey diagram, which supports the coexistence of subpopulations with different chemical compositions. We estimate the mean mass of Anomalous Cepheids ($\sim$1.5M$_{\odot}$) and SX Phoenicis stars ($\sim$1M$_{\odot}$). We discuss in detail the nature of the former. The connections between the properties of the different families of variable stars are discussed in the context of the star formation history of the Sculptor dSph galaxy.

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arXiv2016

The Carina Project. X. On the kinematics of old and intermediate-age stellar populations

We present new radial velocity (RV) measurements of old (horizontal branch) and intermediate-age (red clump) stellar tracers in the Carina dwarf spheroidal. They are based on more than 2,200 low-resolution spectra collected with VIMOS at VLT. The targets are faint (20<V<21.5 mag), but the accuracy at the faintest limit is <9 kms-1. These data were complemented with RV measurements either based on spectra collected with FORS2 and FLAMES/GIRAFFE at VLT or available in the literature. We ended up with a sample of 2748 stars and among them 1389 are candidate Carina stars. We found that the intermediate-age stellar component shows a well defined rotational pattern around the minor axis. The western and the eastern side of the galaxy differ by +5 and -4 km s-1 when compared with the main RV peak. The old stellar component is characterized by a larger RV dispersion and does not show evidence of RV pattern. We compared the observed RV distribution with N-body simulations for a former disky dwarf galaxy orbiting a giant MilkyWay-like galaxy (Lokas et al. 2015). We rotated the simulated galaxy by 60 degrees with respect to the major axis, we kept the observer on orbital plane of the dwarf and extracted a sample of stars similar to the observed one. Observed and predicted Vrot/σ ratios across the central regions are in remarkable agreement. This evidence indicates that Carina was a disky dwarf galaxy that experienced several strong tidal interactions with the Milky Way. Owing to these interactions, Carina transformed from a disky to a prolate spheroid and the rotational velocity transformed into random motions.

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arXiv2016

Sodium abundances of AGB and RGB stars in galactic globular clusters I. Analysis and results of NGC 2808

Galactic globular clusters (GC) are known to have multiple stellar populations and be characterised by similar chemical features, e.g. O-Na anti-correlation. While second-population stars, identified by their Na overabundance, have been found from the main sequence turn-off up to the tip of the red giant branch in various Galactic GCs, asymptotic giant branch (AGB) stars have rarely been targeted. The recent finding that NGC 6752 lacks an Na-rich AGB star has thus triggered new studies on AGB stars in GCs, since this result questions our basic understanding of GC formation and stellar evolution theory. In order to compare the Na abundance distributions of AGB and RGB stars in Galactic GCs and investigate whether the presence of Na-rich stars on the AGB is metallicity-dependent, we obtained the high-resolution spectra with the multi-object high-resolution spectrograph FLAMES on ESO/VLT for a sample of AGB and RGB stars in the Galactic GC NGC 2808. The accurate Na abundances were derived for 31 AGB and 40 RGB stars. We find that NGC 2808 has a mean metallicity of -1.11 $\pm$ 0.08 dex, in good agreement with earlier analyses. Comparable Na abundance dispersions are derived for our AGB and RGB samples, with the AGB stars being slightly more concentrated than the RGB stars. The ratios of Na-poor first-population to Na-rich second-population stars are 45:55 in the AGB sample and 48:52 in the RGB sample. NGC 2808 has Na-rich second-population AGB stars, which turn out to be even more numerous - in relative terms - than their Na-poor AGB counterparts and the Na-rich stars on the RGB. Our findings are well reproduced by the fast rotating massive stars scenario and they do not contradict the recent results that there is not an Na-rich AGB star in NGC 6752. NGC 2808 thus joins the larger group of Galactic GCs for which Na-rich second-population stars on the AGB have recently been found.

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arXiv2016

Probing the early chemical evolution of the Sculptor dSph with purely old stellar tracers

We present the metallicity distribution of a sample of 471 RR Lyrae (RRL) stars in the Sculptor dSph, obtained from the $I$-band Period-Luminosity relation. It is the first time that the early chemical evolution of a dwarf galaxy is characterized in such a detailed and quantitative way, using photometric data alone. We find a broad metallicity distribution (FWHM=0.8 dex) that is peaked at [Fe/H]$\simeq$-1.90 dex, in excellent agreement with literature values obtained from spectroscopic data. Moreover, we are able to directly trace the metallicity gradient out to a radius of $\sim$55 arcmin. We find that in the outer regions (r$>\sim$32 arcmin) the slope of the metallicity gradient from the RRLs (-0.025 dex arcmin$^{-1}$) is comparable to the literature values based on red giant (RG) stars. However, in the central part of Sculptor we do not observe the latter gradients. This suggests that there is a more metal-rich and/or younger population in Sculptor that does not produce RRLs. This scenario is strengthened by the observation of a metal-rich peak in the metallicity distribution of RG stars by other authors, which is not present in the metallicity distribution of the RRLs within the same central area.

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arXiv2016

Before the Bar: Kinematic Detection of A Spheroidal Metal-Poor Bulge Component

We present 947 radial velocities of RR Lyrae variable stars in four fields located toward the Galactic bulge, observed within the data from the ongoing Bulge RR Lyrae Radial Velocity Assay (BRAVA-RR). We show that these RR Lyrae stars exhibit hot kinematics and null or negligible rotation and are therefore members of a separate population from the bar/pseudobulge that currently dominates the mass and luminosity of the inner Galaxy. Our RR Lyrae stars predate these structures, and have metallicities, kinematics, and spatial distribution that are consistent with a "classical" bulge, although we cannot yet completely rule out the possibility that they are the metal-poor tail of a more metal rich ([Fe/H] ~ -1 dex) halo-bulge population. The complete catalog of radial velocities for the BRAVA-RR stars is also published electronically.

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arXiv2016

Pulsating hot O subdwarfs in Omega Cen: mapping a unique instability strip on the Extreme Horizontal Branch

We present an extensive survey for rapid pulsators among Extreme Horizontal Branch (EHB) stars in omega Cen. The observations performed consist of nearly 100 hours of time-series photometry, as well as low-resolution spectroscopy. We obtained photometry for some 300 EHB stars. Based on the spectroscopy, we derive reliable values of log g, Teff and log(N(He)/N(H)) for 38 targets, as well as estimates of the effective temperature for another nine targets. The survey uncovered a total of five rapid variables with multi-periodic oscillations between 85 and 125 s. Spectroscopically, they form a homogeneous group of hydrogen-rich subdwarf O stars clustered between 48,000 and 54,000 K. For each of the variables we are able to measure between two and three significant pulsations believed to constitute independent harmonic oscillations. In addition to the rapid variables, we found an EHB star with an apparently periodic luminosity variation of ~2700 s, which we tentatively suggest may be caused by ellipsoidal variations in a close binary. Using the overlapping photometry and spectroscopy sample we are able to map an empirical omega Cen instability strip. This can be directly compared to the pulsation driving predicted from the Montreal "second-generation" models. We find that the region where p-mode excitation occurs is bifurcated, and the well-known instability strip between 29,000-36,000 K where the rapid subdwarf B pulsators are found is complemented by a second one above 50,000 K. While significant challenges remain at the quantitative level, we believe that the same kappa-mechanism that drives the pulsations in hot B subdwarfs is also responsible for the excitation of the rapid oscillations observed in the omega Cen variables.

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arXiv2015

GeMS MCAO observations of the Galactic globular cluster NGC 2808: the absolute age

Globular clusters are the oldest stellar systems in the Milky Way and probe the early epoch of the Galaxy formation. However, the uncertainties on their absolute age are still too large to soundly constrain how the Galactic structures have assembled. The aim of this work is to obtain an accurate estimate of the absolute age of the globular cluster NGC 2808 using deep IR data obtained with the multi conjugate adaptive optics system operating at the Gemini South telescope (GeMS). This exquisite photometry, combined with that obtained in V and I bands with HST, allowed us the detection of the faint Main Sequence Knee feature in NGC 2808 colour magnitude diagram. The difference between this point and the main sequence turn off is a good age estimator and provides ages with unprecedented accuracy. We found that NGC 2808 has an age of t=10.9\pm0.7 (intrinsic) \pm0.45 (metallicity term) Gyr. A possible contamination by He-enhanced population could make the cluster up to 0.25 Gyr older. Although this age estimate agrees with the age coming from the classical turn off method (t=11.0 Gyr), its uncertainty is a factor ~3 better, since it avoids systematics in reddening, distance assumptions and photometric zero points determination. The final absolute age indicates that NGC 2808 is slightly younger than other Galactic globular clusters with similar metallicity.

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arXiv2015

On the neutron-capture elements across the Galactic thin disk using Cepheids

We present new accurate abundances for five neutron-capture (Y, La, Ce, Nd, Eu) elements in 73 classical Cepheids located across the Galactic thin disk. Individual abundances are based on high spectral resolution (R ~ 38,000) and high signal-to-noise ratio (S/N ~ 50-300) spectra collected with UVES at ESO VLT for the DIONYSOS project. Taking account for similar Cepheid abundances provided either by our group (111 stars) or available in the literature, we end up with a sample of 435 Cepheids covering a broad range in iron abundances (-1.6 < [Fe/H] < 0.6). We found, using homogeneous individual distances and abundance scales, well defined gradients for the above elements. However, the slope of the light s-process element (Y) is at least a factor of two steeper than the slopes of heavy s- (La, Ce, Nd) and r- (Eu) process elements. The s to r abundance ratio ([La/Eu]) of Cepheids shows a well defined anticorrelation with of both Eu and Fe. On the other hand, Galactic field stars attain an almost constant value and only when they approach solar iron abundance display a mild enhancement in La. The [Y/Eu] ratio shows a mild evidence of a correlation with Eu and, in particular, with iron abundance for field Galactic stars. We also investigated the s-process index - [hs/ls] - and we found a well defined anticorrelation, as expected, between [La/Y] and iron abundance. Moreover, we found a strong correlation between [La/Y] and [La/Fe] and, in particular, a clear separation between Galactic and Sagittarius red giants. Finally, the comparison between predictions for low-mass asymptotic giant branch stars and the observed [La/Y] ratio indicate a very good agreement over the entire metallicity range covered by Cepheids. However, the observed spread, at fixed iron content, is larger than predicted by current models.

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arXiv2015

The Carina Project IX: on Hydrogen and helium burning variables

We present new multi-band (UBVI) time-series data of helium burning variables in the Carina dwarf spheroidal galaxy. The current sample includes 92 RR Lyrae-six of them are new identifications-and 20 Anomalous Cepheids, one of which is new identification. The analysis of the Bailey diagram shows that the luminosity amplitude of the first overtone component in double-mode variables is located along the long-period tail of regular first overtone variables, while the fundamental component is located along the short-period tale of regular fundamental variables. This evidence further supports the transitional nature of these objects. Moreover, the distribution of Carina double-mode variables in the Petersen diagram (P_1/P_0 vs P_0) is similar to metal-poor globulars (M15, M68), to the dwarf spheroidal Draco and to the Galactic Halo. This suggests that the Carina old stellar population is metal-poor and affected by a small spread in metallicity. We use trigonometric parallaxes for five field RR Lyrae stars to provide an independent estimate of the Carina distance using the observed reddening free Period--Wesenheit [PW, (BV)] relation. Theory and observations indicate that this diagnostic is independent of metallicity. We found a true distance modulus of μ=20.01\pm0.02 (standard error of the mean) \pm0.05 (standard deviation) mag. We also provided independent estimates of the Carina true distance modulus using four predicted PW relations (BV, BI, VI, BVI) and we found: μ=(20.08\pm0.007\pm0.07) mag, μ=(20.06\pm0.006\pm0.06) mag, μ=(20.07\pm0.008\pm0.08) mag and μ=(20.06\pm0.006\pm0.06) mag. Finally, we identified more than 100 new SX Phoenicis stars that together with those already known in the literature (340) make Carina a fundamental laboratory to constrain the evolutionary and pulsation properties of these transitional variables.

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arXiv2015

Towards Precision Photometry with Extremely Large Telescopes: the Double Subgiant Branch of NGC 1851

The Extremely Large Telescopes currently under construction have a collecting area that is an order of magnitude larger than the present largest optical telescopes. For seeing-limited observations the performance will scale as the collecting area but, with the successful use of adaptive optics, for many applications it will scale as $D^4$ (where $D$ is the diameter of the primary mirror). Central to the success of the ELTs, therefore, is the successful use of multi-conjugate adaptive optics (MCAO) that applies a high degree correction over a field of view larger than the few arcseconds that limits classical adaptive optics systems. In this letter, we report on the analysis of crowded field images taken on the central region of the Galactic globular cluster NGC 1851 in $K_s$ band using GeMS at the Gemini South telescope, the only science-grade MCAO system in operation. We use this cluster as a benchmark to verify the ability to achieve precise near-infrared photometry by presenting the deepest $K_s$ photometry in crowded fields ever obtained from the ground. We construct a colour-magnitude diagram in combination with the F606W band from HST/ACS. As well as detecting the "knee" in the lower main sequence at $K_s\simeq20.5$, we also detect the double subgiant branch of NGC 1851, that demonstrates the high photometric accuracy of GeMS in crowded fields.

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arXiv2015

Variable Stars in Local Group Galaxies. I: Tracing the Early Chemical Enrichment and Radial Gradients in the Sculptor dSph with RR Lyrae Stars

We identified and characterized the largest (536) RR Lyrae (RRL) sample in a Milky Way dSph satellite (Sculptor) based on optical photometry data collected over $\sim$24 years. The RRLs display a spread in V-magnitude ($\sim$0.35 mag) which appears larger than photometric errors and the horizontal branch (HB) luminosity evolution of a mono-metallic population. Using several calibrations of two different reddening free and metal independent Period-Wesenheit relations we provide a new distance estimate $μ$=19.62 mag ($σ_μ$=0.04 mag) that agrees well with literature estimates. We constrained the metallicity distribution of the old population, using the $M_I$ Period-Luminosity relation, and we found that it ranges from -2.3 to -1.5 dex. The current estimate is narrower than suggested by low and intermediate spectroscopy of RGBs ($Δ$[Fe/H] $\le$ 1.5). We also investigated the HB morphology as a function of the galactocentric distance. The HB in the innermost regions is dominated by red HB stars and by RRLs, consistent with a more metal-rich population, while in the outermost regions it is dominated by blue HB stars and RRLs typical of a metal-poor population. Our results suggest that fast chemical evolution occurred in Sculptor, and that the radial gradients were in place at an early epoch.

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arXiv2015

The absolute age of the globular cluster M15 using near-infrared adaptive optics images from PISCES/LBT

We present deep near-infrared (NIR) J, Ks photometry of the old, metal-poor Galactic globular cluster M\,15 obtained with images collected with the LUCI1 and PISCES cameras available at the Large Binocular Telescope (LBT). We show how the use of First Light Adaptive Optics system coupled with the (FLAO) PISCES camera allows us to improve the limiting magnitude by ~2 mag in Ks. By analyzing archival HST data, we demonstrate that the quality of the LBT/PISCES color magnitude diagram is fully comparable with analogous space-based data. The smaller field of view is balanced by the shorter exposure time required to reach a similar photometric limit. We investigated the absolute age of M\,15 by means of two methods: i) by determining the age from the position of the main sequence turn-off; and ii) by the magnitude difference between the MSTO and the well-defined knee detected along the faint portion of the MS. We derive consistent values of the absolute age of M15, that is 12.9+-2.6 Gyr and 13.3+-1.1 Gyr, respectively.

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arXiv2015

Blue straggler masses from pulsation properties. II. Topology of the Instability Strip

We present a new set of nonlinear, convective radial pulsation models for main sequence stars computed assuming three metallicities: Z=0.0001, 0.001 and 0.008. These chemical compositions bracket the metallicity of stellar systems hosting SX Phoenicis stars (SXPs or pulsating Blue Stragglers), namely Galactic globular clusters and nearby dwarf spheroidals. Stellar masses and luminosities of the pulsation models are based on alpha--enhanced evolutionary tracks from the BASTI website. We are able to define the topology of the instability strip (IS), and in turn the pulsation relations for the first four pulsation modes. We found that third overtones approach a stable nonlinear limit cycle. Predicted and empirical IS agree quite well in the case of 49 SXPs belonging to omega Cen. We used theoretical Period-Luminosity relations in B,V bands to identify their pulsation mode. We assumed Z=0.001 and Z=0.008 as mean metallicities of SXPs in omega Cen. We found respectively 13-15 fundamental, 22-6 first and 9-4 second overtone modes. Five are unstable in the third overtone mode only for Z=0.001. Using the above mode identification and applying the proper mass-dependent Period-Luminosity relations we found masses ranging from ~1.0 to 1.2 Mo ( =1.12, sigma=0.04 Mo) and from ~1.2 to 1.5 Mo ( =1.33, sigma=0.03 Mo) for Z=0.001 and 0.008 respectively. Our investigation supports the use of evolutionary tracks to estimate of SXP masses. We will extend our analysis to higher Helium content that may have an impact in our understanding of the BSS formation scenario.

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arXiv2015

The Carina Project. VIII. The α-element abundances

We have performed a new abundance analysis of Carina Red Giant (RG) stars from spectroscopic data collected with UVES (high resolution) and FLAMES/GIRAFFE (high and medium resolution) at ESO/VLT. The former sample includes 44 RGs, while the latter consists of 65 (high) and ~800 (medium resolution) RGs, covering a significant fraction of the galaxy's RG branch (RGB), and red clump stars. To improve the abundance analysis at the faint magnitude limit, the FLAMES/GIRAFFE data were divided into ten surface gravity and effective temperature bins. The spectra of the stars belonging to the same gravity/temperature bin were stacked. This approach allowed us to increase by at least a factor of five the signal-to-noise ratio in the faint limit (V>20.5mag). We took advantage of the new photometry index cU,B,I introduced by Monelli et al. (2014), as an age and probably a metallicity indicator, to split stars along the RGB. These two stellar populations display distinct [Fe/H] and [Mg/H] distributions: their mean Fe abundances are -2.15$\pm$0.06dex (sig=0.28), and -1.75$\pm$0.03dex (sig=0.21), respectively. The two iron distributions differ at the 75% level. This supports preliminary results by Lemasle et al. (2012) and by Monelli et al. (2014). Moreover, we found that the old and intermediate-age stellar populations have mean [Mg/H] abundances of -1.91$\pm$0.05dex (sig=0.22) and -1.35$\pm$0.03dex (sig=0.22); these differ at the 83% level. Carina's α-element abundances agree, within 1sigma, with similar abundances for field Halo stars and for cluster (Galactic, Magellanic) stars. The same outcome applies to nearby dwarf spheroidals and ultra-faint dwarf galaxies, in the iron range covered by Carina stars. Finally, we found evidence of a clear correlation between Na and O abundances, thus suggesting that Carina's chemical enrichment history is quite different than in the globular clusters.

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arXiv2015

On the distance of the globular cluster M4 (NGC 6121) using RR Lyrae stars: II. Mid-infrared period-luminosity relations

New mid-infrared period-luminosity (PL) relations are presented for \rrl{} variables in the globular cluster M4 (NGC 6121). Accurate photometry was obtained for 37 \rrl{} variables using observations from the Infrared Array Camera onboard the Spitzer Space Telescope. The dispersion of M4's PL relations is 0.056, and the uncertainty in the slope is 0.11 mag. Additionally, weestablished calibrated PL relations at 3.6 and 4.5~\micron{} using published Hubble Space Telescopegeometric parallaxes of five Galactic \rrl{} stars. The resulting band-averaged distance modulus for M4 is $ μ= 11.399 \pm 0.007 \textrm{(stat)} \pm 0.080 \textrm{(syst)} \pm 0.015 \textrm{(cal)} \pm 0.020 \textrm{(ext)}$. The systematic uncertainty will be greatly reduced when parallaxes of more stars become available from the GAIA mission. Optical and infrared period-color (PC) relations are also presented, and the lack of a MIR PC relation suggests that \rrl{} stars are not affected by CO absorptionin the 4.5~\micron{} band.

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