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24 paper(s) to start with

preprint2016arXiv

Mirror dark matter will be confirmed or excluded by XENON1T

Mirror dark matter, where dark matter resides in a hidden sector exactly isomorphic to the standard model, can be probed via direct detection experiments by both nuclear and electron recoils if the kinetic mixing interaction exists. In fact, the kinetic mixing interaction appears to be a prerequisite for consistent small scale structure: Mirror dark matter halos around spiral galaxies are dissipative - losing energy via dark photon emission. This ongoing energy loss requires a substantial energy input, which can be sourced from ordinary supernovae via kinetic mixing induced processes in the supernova's core. Astrophysical considerations thereby give a lower limit on the kinetic mixing strength, and indeed lower limits on both nuclear and electron recoil rates in direct detection experiments can be estimated. We show here that potentially all of the viable parameter space will be probed in forthcoming XENON experiments including LUX and XENON1T. Thus, we anticipate that these experiments will provide a definitive test of the mirror dark matter hypothesis.

preprint2016arXiv

The Burrell Schmidt Deep Virgo Survey: Tidal Debris, Galaxy Halos, and Diffuse Intracluster Light in the Virgo Cluster

We present a deep imaging survey of the Virgo Cluster, designed to study the connection between cluster galaxies and Virgo's diffuse intracluster light (ICL). Our observations span roughly 16 square degrees and reach a 3-sigma depth of mu(B)=29.5 and mu(V)=28.5 mag/arcsec^2. At these depths, the limiting systematic uncertainties are astrophysical: scattered starlight from foreground Galactic dust, and variations in faint background sources. The dust-scattered starlight is well-traced by deep far-infrared imaging, making it distinguishable from true Virgo diffuse light. Our imaging maps the Virgo core around M87 and the adjacent M86/M84 region, in subcluster B around M49, and in the more distant W' cloud around NGC 4365. Most of the detected ICL is found in the Virgo core and within the W' cloud, with little evidence for extensive ICL in subcluster B. The large amount of diffuse light seen in the infalling W' cloud likely illustrates the importance of the group environment for generating ICL. The bulk of the detected ICL is fairly red (B-V=0.7-0.9), indicative of old stellar populations. We estimate a total Virgo ICL fraction of 7-15%, somewhat smaller than expected

preprint2016arXiv

A correlation between chemistry, polarization and dust properties in the Pipe Nebula starless core FeSt 1-457

Pre-stellar cores within molecular clouds provide the very initial conditions in which stars are formed. We use the IRAM 30m telescope and the PdBI to study the chemical and physical properties of the starless core FeSt 1-457 (Core 109), in the Pipe nebula. We fit the hyperfine structure of the N2H+(1-0) IRAM 30m data. This allow us to measure with high precision the velocity field, line widths and opacity and derive the excitation temperature and column density in the core. We use a modified Bonnor-Ebert sphere model adding a temperature gradient towards the center to fit the 1.2 mm continuum emission and visual extinction maps. Using this model, we estimate the abundances of the N2H+ and the rest of molecular lines detected in the 30 GHz wide line survey performed at 3 mm with IRAM 30m using ARTIST software. The core presents a rich chemistry with emission from early (C3H2, HCN, CS) and late-time molecules (e.g., N2H+), with a clear chemical spatial differentiation for nitrogen, oxygen and sulphurated molecules. For most of the molecules detected (HCN, HCO+, CH3OH, CS, SO, 13CO and C18O), abundances are best fitted with three values, presenting a clear decrease of abundance of at

preprint2017arXiv

Connecting the new H.E.S.S. diffuse emission at the Galactic center with the Fermi GeV excess: a combination of millisecond pulsars and heavy dark matter?

The H.E.S.S. collaboration has reported a high-energy spherically symmetric diffuse gamma-ray emission in the inner 50 pc of the Milky Way, up to ~ 50 TeV. Here we propose a leptonic model which provides an alternative to the hadronic scenario presented by the H.E.S.S. collaboration, and connects the newly reported TeV emission to the Fermi-LAT Galactic center GeV excess. Our model relies on a combination of inverse Compton emission from a population of millisecond pulsars---which can account for the GeV excess---and a supermassive black hole-induced spike of heavy (~ 60 TeV) dark matter particles annihilating into electrons with a sub-thermal cross-section. With an up-to-date interstellar radiation field, as well as a standard magnetic field and diffusion set-up, our model accounts for the spectral morphology of the detected emission. Moreover, we show that the dark matter induced emission reproduces the spatial morphology of the H.E.S.S. signal above ~ 10 TeV, while we obtain a slightly more extended component from pulsars at lower energies, which could be used as a prediction for future H.E.S.S. observations.

preprint2016arXiv

The Local Bubble in the interstellar medium and the origin of the low energy cosmic rays

An analysis of the energy spectra of cosmic rays and particularly the precise data from the AMS-02 experiment support the view about the important role of the Local Bubble in the nearby interstellar medium. It is suggested that the bulk of cosmic rays below about 200 GV of rigidity (momentum/charge ratio) comes from the modest number of supernova remnants in the Local Bubble which appear to have occurred some $10^6$ years ago and contributed to its formation. At higher rigidities the contribution from a 'Local Source', a single supernova remnant generated some $10^5$ years ago seems to dominate up to, at least 1000 GV.

preprint2013arXiv

Supermassive Black Holes and Nuclear Star Clusters: Connection with the Host Galaxy Kinematics and Color

We consider the relationship between the masses of the central objects in disky galaxies - supermassive black holes (SMBHs) and nuclear star clusters (NCs) - and various parameters of parent galaxies: velocity of rotation $V_{(2)}$ at $R= 2$ kpc, maximal velocity of rotation $V_{\textrm{max}}$, the indicative dynamical mass $M_{25}$, the total mass of the stellar population $M_{*}$, and the total color index ($B{-}V$). The mass of nuclear clusters $M_{\rm nc}$ correlates more closely with the kinematic parameters and total mass of galaxies than the mass of central black holes $M_{\rm bh}$, including correlation with the velocity $V_{\textrm{max}}$, which characterizes the virial mass of the dark halo. On average, lenticular galaxies are distinguished by higher masses $M_{\rm bh}$ compared to other types of galaxies with similar characteristics. The dependence of masses of central objects on the color index is bimodal: galaxies of the red group (red-sequence), which have ($B{-}V) > 0.6{-}0.7$, being mostly early-type galaxies, differ from bluer galaxies, by higher values of $M_{\rm nc}$ and $M_{\rm bh}$. The red-group galaxies have systematically higher $M_{\rm bh}$ values, even whe

preprint2016arXiv

Spectral Energy Distribution Mapping of Two Elliptical Galaxies on sub-kpc scales

We use high-resolution Herschel-PACS data of 2 nearby elliptical galaxies, IC1459 & NGC2768 to characterize their dust and stellar content. IC1459 & NGC2768 have an unusually large amount of dust for elliptical galaxies (1-3 x 10^5 Msun), this dust is also not distributed along the stellar content. Using data from GALEX (ultraviolet) to PACS (far-infrared), we analyze the spectral energy distribution (SED) of these galaxies with CIGALEMC as a function of the projected position, binning images in 7.2" pixels. From this analysis, we derive maps of SED parameters, such as the metallicity, the stellar mass, the fraction of young star and the dust mass. The larger amount of dust in FIR maps seems related in our model to a larger fraction of young stars which can reach up to 4% in the dustier area. The young stellar population is fitted as a recent (~ 0.5 Gyr) short burst of star formation for both galaxies. The metallicities, which are fairly large at the center of both galaxies, decrease with the radial distance with fairly steep gradient for elliptical galaxies.

preprint2016arXiv

The Chandra Deep Field-South Survey: 7 Ms Source Catalogs

We present X-ray source catalogs for the $\approx7$ Ms exposure of the Chandra Deep Field-South (CDF-S), which covers a total area of 484.2 arcmin$^2$. Utilizing WAVDETECT for initial source detection and ACIS Extract for photometric extraction and significance assessment, we create a main source catalog containing 1008 sources that are detected in up to three X-ray bands: 0.5-7.0 keV, 0.5-2.0 keV, and 2-7 keV. A supplementary source catalog is also provided including 47 lower-significance sources that have bright ($K_s\le23$) near-infrared counterparts. We identify multiwavelength counterparts for 992 (98.4%) of the main-catalog sources, and we collect redshifts for 986 of these sources, including 653 spectroscopic redshifts and 333 photometric redshifts. Based on the X-ray and multiwavelength properties, we identify 711 active galactic nuclei (AGNs) from the main-catalog sources. Compared to the previous $\approx4$ Ms CDF-S catalogs, 291 of the main-catalog sources are new detections. We have achieved unprecedented X-ray sensitivity with average flux limits over the central $\approx1$ arcmin$^2$ region of $\approx1.9\times10^{-17}$, $6.4\times10^{-18}$, and $2.7\times10^{-17}$ er

preprint2016arXiv

Superbubbles in the Multiphase ISM and the Loading of Galactic Winds

We use numerical simulations to analyze the evolution and properties of superbubbles (SBs), driven by multiple supernovae (SNe), that propagate into the two-phase (warm/cold), cloudy interstellar medium (ISM). We consider a range of mean background densities n_avg=0.1-10 cm^{-3} and intervals between SNe dt_sn=0.01-1 Myr, and follow each SB until the radius reaches (1-2)H, where H is the characteristic ISM disk thickness. Except for embedded dense clouds, each SB is hot until a time t_sf,m when the shocked warm gas at the outer front cools and forms an overdense shell. Subsequently, diffuse gas in the SB interior remains at T_h 10^6-10^7K with expansion velocity v_h~10^2-10^3km/s (both highest for low dt_sn). At late times, the warm shell gas velocities are several 10's to ~100km/s. While shell velocities are too low to escape from a massive galaxy, they are high enough to remove substantial mass from dwarfs. Dense clouds are also accelerated, reaching a few to 10's of km/s. We measure the mass in hot gas per SN, M_h/N_SN, and the total radial momentum of the bubble per SN, p_b/N_SN. After t_sf,m, M_h/N_SN 10-100M_sun (highest for low n_avg), while p_b/N_SN 0.7-3x10^5M_sun

preprint2016arXiv

Kinematics of Ultra-High-Velocity Gas in the Expanding Molecular Shell adjacent to the W44 Supernova Remnant

We mapped the ultra-high-velocity feature (the "Bullet") detected in the expanding molecular shell associated with the W44 supernova remnant using the Nobeyama Radio Observatory 45-m telescope and the ASTE 10-m telescope. The Bullet clearly appears in the CO ${\it J}$=1-0, CO ${\it J}$=3-2, CO ${\it J}$=4-3, and HCO$^+$ ${\it J}$=1-0 maps with a compact appearance ($0.5\times 0.8$ pc$^2$) and an extremely broad velocity width ($ΔV\!\simeq\!100 \ \rm km \, s ^{-1}$). The line intensities indicate that the Bullet has a higher density and temperature than those in the expanding molecular shell. The kinetic energy of the Bullet amounts to $10^{48.0} \ {\rm erg}$ which is approximately 1.5 orders of magnitude greater than the kinetic energy shared to the small solid angle of it. Two possible formation scenarios with an inactive isolated black hole (BH) are presented.

preprint2016arXiv

Gemini Near Infrared Field Spectrograph Observations of the Seyfert 2 Galaxy Mrk 573: In Situ Acceleration of Ionized and Molecular Gas Off Fueling Flows

We present near-infrared and optical emission-line and stellar kinematics of the Seyfert 2 galaxy Mrk 573 using the Near-Infrared Field Spectrograph (NIFS) at Gemini North and Dual Imaging Spectrograph (DIS) at Apache Point Observatory, respectively. By obtaining full kinematic maps of the infrared ionized and molecular gas and stellar kinematics in a 700 x 2100 pc^2 circumnuclear region of Mrk 573, we find that kinematics within the Narrow-Line Region (NLR) are largely due to a combination of both rotation and in situ acceleration of material originating in the host disk. Combining these observations with large-scale, optical long-slit spectroscopy that traces ionized gas emission out to several kpcs, we find that rotation kinematics dominate the majority of the gas. We find that outflowing gas extends to distances less than 1 kpc, suggesting that outflows in Seyfert galaxies may not be powerful enough to evacuate their entire bulges.

preprint2016arXiv

The Evolution of Star Formation Activity in Cluster Galaxies Over $0.15<z<1.5$

We explore 7.5 billion years of evolution in the star formation activity of massive ($M_{\star}>10^{10.1}\,M_{\odot}$) cluster galaxies using a sample of 25 clusters over $0.15<z<1$ from the Cluster Lensing And Supernova survey with Hubble and 11 clusters over $1<z<1.5$ from the IRAC Shallow Cluster Survey. Galaxy morphologies are determined visually using high-resolution Hubble Space Telescope images. Using the spectral energy distribution fitting code CIGALE, we measure star formation rates, stellar masses, and 4000 Å break strengths. The latter are used to separate quiescent and star-forming galaxies (SFGs). From $z\sim1.3$ to $z\sim0.2$, the specific star formation rate (sSFR) of cluster SFGs and quiescent galaxies decreases by factors of three and four, respectively. Over the same redshift range, the sSFR of the entire cluster population declines by a factor of 11, from $0.48\pm0.06\;\mathrm{Gyr}^{-1}$ to $0.043\pm0.009\;\mathrm{Gyr}^{-1}$. This strong overall sSFR evolution is driven by the growth of the quiescent population over time; the fraction of quiescent cluster galaxies increases from $28^{+8}_{-19}\%$ to $88^{+5}_{-4}\%$ over $z\sim1.3\rightarrow0.2$. The majority of

preprint2016arXiv

Probing WHIM around Galaxy Clusters with Fast Radio Bursts and the Sunyaev-Zel'dovich effect

We propose a new method to probe the Warm Hot Intergalactic Medium (WHIM) beyond the virial radius (R_200) of a cluster of galaxies, where X-ray observations are not easily achievable. In this method, we use dispersion measures (DMs) of Fast Radio Bursts (FRBs) that appear behind the cluster and the Sunyaev-Zel'dovich (SZ) effect towards the cluster. The DMs reflect the density of the intracluster medium (ICM) including the WHIM. If we observe a sufficient number of FRBs in the direction of the cluster, we can derive the density profile from the DMs. Similarly, we can derive the pressure profile from the SZ effect. By combining the density and the pressure profiles, the temperature profile can be obtained. Based on mock observations of nearby clusters, we find that the density of the WHIM can be determined even at > 2 R_200 from the cluster center when FRB observations with the Square Kilometre Array (SKA) become available. The temperature can be derived out to r~ 1.5 R_200, and the radius is limited by the current sensitivity of SZ observations.

preprint2016arXiv

The Geometry of the Infrared and X-ray Obscurer in a Dusty Hyperluminous Quasar

We study the geometry of the AGN obscurer in IRAS 09104+4109, an IR-luminous, radio-intermediate FR-I source at $z=0.442$, using infrared data from Spitzer and Herschel, X-ray data from Nustar, Swift, Suzaku, and Chandra, and an optical spectrum from Palomar. The infrared data imply a total rest-frame 1-1000$μ$m luminosity of $5.5\times10^{46}$erg s$^{-1}$ and require both an AGN torus and starburst model. The AGN torus has an anisotropy-corrected IR luminosity of $4.9\times10^{46}$erg s$^{-1}$, and a viewing angle and half opening angle both of approximately $36$ degrees from pole-on. The starburst has a star formation rate of $(110\pm34)$M$_{\odot}$ yr$^{-1}$ and an age of $<50$Myr. These results are consistent with two epochs of luminous activity in 09104: one approximately $150$Myr ago, and one ongoing. The X-ray data suggest a photon index of $Γ\simeq 1.8$ and a line-of-sight column of $N_{\rm H} \simeq 5\times10^{23}$cm$^{-2}$. This argues against a reflection-dominated hard X-ray spectrum, which would have implied a much higher $N_{\rm H}$ and luminosity. The X-ray and infrared data are consistent with a bolometric AGN luminosity of $L_{\rm bol}\sim(0.5-2.5)\times10^{47}$erg

preprint2016arXiv

Carbon monoxide in an extremely metal-poor galaxy

Extremely metal-poor galaxies with metallicity below 10% of the solar value in the local universe are the best analogues to investigating the interstellar medium at a quasi-primitive environment in the early universe. In spite of the ongoing formation of stars in these galaxies, the presence of molecular gas (which is known to provide the material reservoir for star formation in galaxies, such as our Milky Way) remains unclear. Here, we report the detection of carbon monoxide (CO), the primary tracer of molecular gas, in a galaxy with 7% solar metallicity, with additional detections in two galaxies at higher metallicities. Such detections offer direct evidence for the existence of molecular gas in these galaxies that contain few metals. Using archived infrared data, it is shown that the molecular gas mass per CO luminosity at extremely low metallicity is approximately one-thousand times the Milky Way value.

preprint2016arXiv

Mass-to-Light versus Color Relations for Dwarf Irregular Galaxies

We have determined new relations between $UBV$ colors and mass-to-light ratios ($M/L$) for dwarf irregular (dIrr) galaxies, as well as for transformed $g^\prime - r^\prime$. These $M/L$ to color relations (MLCRs) are based on stellar mass density profiles determined for 34 LITTLE THINGS dwarfs from spectral energy distribution fitting to multi-wavelength surface photometry in passbands from the FUV to the NIR. These relations can be used to determine stellar masses in dIrr galaxies for situations where other determinations of stellar mass are not possible. Our MLCRs are shallower than comparable MLCRs in the literature determined for spiral galaxies. We divided our dwarf data into four metallicity bins and found indications of a steepening of the MLCR with increased oxygen abundance, perhaps due to more line blanketing occurring at higher metallicity.

preprint2016arXiv

Angular Momentum of Dwarf Galaxies

We present measurements of baryonic mass Mb and specific angular momentum (sAM) jb in 14 rotating dwarf Irregular (dIrr) galaxies from the LITTLE THINGS sample. These measurements, based on 21cm kinematic data from the Very Large Array and stellar mass maps from the Spitzer Space Telescope, extend previous AM measurements by more than two orders of magnitude in Mb. The dwarf galaxies show systematically higher jb values than expected from the jb~Mb^{2/3} scaling of spiral galaxies, representative of a scale-free galaxy formation scenario. This offset can be explained by decreasing baryon mass fractions fM=Mb Mdyn (where Mdyn is the dynamical mass) with decreasing Mb (for Mb<10^{11}Msun). We find that the sAM of neutral atomic hydrogen HI alone is about 2.5 times higher than that of the stars. The M-j relation of HI is significantly steeper than that of the stars, as a direct consequence of the systematic variation of the HI fraction with Mb.

preprint2014arXiv

A Universal Power-law Profile of Pseudo-Phase-Space Density-like Quantities in Elliptical Galaxies

We study profiles of mass density, velocity dispersion (VD), and their combination using $\sim 2000$ nearly spherical and rotation-free SDSS galaxies. For observational stellar mass density $ρ_{\star}(r)$ we consider a range of dark matter (DM) distribution $ρ_{\rm{DM}}(r)$ and VD anisotropy $β(r)$ to investigate radial stellar VD $σ_{\rm\star r}(r)$ using the spherical Jeans equation. While mass and VD profiles vary appreciably depending on DM distribution and anisotropy, the pseudo-phase-space density-like combination $ρ(r)/σ_{\rm\star r}^3(r)$ with total density $ρ(r)= ρ_{\star}(r)+ρ_{\rm{DM}}(r)$ is nearly universal. In the optical region the minus of its logarithmic slope has a mean value of $\langleχ\rangle\approx 1.86$--$1.90$ with a galaxy-to-galaxy rms scatter of $\approx 0.04$--$0.06$, which is a few times smaller than that of $ρ(r)$ profiles. The scatter of $χ$ can be increased by invoking wildly varying anisotropies that are, however, less likely because they would produce too large a scatter of line-of-sight VD profiles. As an independent check of this universality we analyze stellar orbit-based dynamical models of 15 ETGs of Coma cluster provided by J. Thomas. Coma ET

preprint2016arXiv

Two-fluid dusty shocks: simple benchmarking problems and applications to protoplanetary discs

The key role that dust plays in the interstellar medium has motivated the development of numerical codes designed to study the coupled evolution of dust and gas in systems such as turbulent molecular clouds and protoplanetary discs. Drift between dust and gas has proven to be important as well as numerically challenging. We provide simple benchmarking problems for dusty gas codes by numerically solving the two-fluid dust-gas equations for steady, plane-parallel shock waves. The two distinct shock solutions to these equations allow a numerical code to test different forms of drag between the two fluids, the strength of that drag and the dust to gas ratio. We also provide an astrophysical application of J-type dust-gas shocks to studying the structure of accretion shocks onto protoplanetary discs. We find that two-fluid effects are most important for grains larger than 1 um, and that the peak dust temperature within an accretion shock provides a signature of the dust-to-gas ratio of the infalling material.

preprint2016arXiv

The quenched mass portion of star-forming galaxies and the origin of the star formation sequence slope

Observationally, a massive disk galaxy can harbor a bulge component that is comparably inactive as a quiescent galaxy (QG). It has been speculated that the quenched component contained in star-forming galaxies (SFGs) is the reason why the star formation main sequence (MS) has a shallow slope at high masses. In this paper, we present a toy model to quantify the quenched mass portion of SFGs ($f_{\rm Q}$) at fixed stellar mass ($M_{\ast}$) and to reconcile the MS slopes both in the low and the high mass regimes. In this model, each SFG is composed by a star-forming plus a quenched component. The mass of the star-forming component ($M_{\rm SF}$) correlates with the star formation rate (SFR) following a relation SFR $\propto M_{\rm SF}^{α_{\rm SF}}$, where $α_{\rm SF}\sim 1.0$ . The quenched component contributes to the stellar mass but does not to the SFR. It is thus possible to quantify $f_{\rm Q}$ based on the departure of the observed MS slope $α$ from $α_{\rm SF}$. Adopting the redshift-dependent MS slope reported by \citet{Whitaker 2014}, we explore the evolution of the $f_{\rm Q}-M_{\ast}$ relations over $z=[0.5,2.5]$. We find that Milky-Way mass SFGs (with $M_{\ast}\approx 10^{

preprint2017arXiv

A merger in the dusty, $z=7.5$ galaxy A1689-zD1?

The gravitationally-lensed galaxy A1689-zD1 is one of the most distant spectroscopically confirmed sources ($z=7.5$). It is the earliest known galaxy where the interstellar medium (ISM) has been detected; dust emission was detected with the Atacama Large Millimetre Array (ALMA). A1689-zD1 is also unusual among high-redshift dust emitters as it is a sub-L* galaxy and is therefore a good prospect for the detection of gaseous ISM in a more typical galaxy at this redshift. We observed A1689-zD1 with ALMA in bands 6 and 7 and with the Green Bank Telescope (GBT) in band $Q$. To study the structure of A1689-zD1, we map the mm thermal dust emission and find two spatial components with sizes about $0.4-1.7$\,kpc (lensing-corrected). The rough spatial morphology is similar to what is observed in the near-infrared with {\it HST} and points to a perturbed dynamical state, perhaps indicative of a major merger or a disc in early formation. The ALMA photometry is used to constrain the far-infrared spectral energy distribution, yielding a dust temperature ($T_{\rm dust} \sim 35$--$45$\,K for $β= 1.5-2$). We do not detect the CO(3-2) line in the GBT data with a 95\% upper limit of 0.3\,mJy observed

preprint2016arXiv

Following The Cosmic Evolution Of Pristine Gas I: Implications For Milky Way Halo Stars

We make use of new subgrid model of turbulent mixing to accurately follow the cosmological evolution of the first stars, the mixing of their supernova ejecta, and the impact on the chemical composition of the Galactic Halo. Using the cosmological adaptive mesh refinement code RAMSES, we implement a model for the pollution of pristine gas as described in Pan et al. Tracking the metallicity of Pop III stars with metallicities below a critical value allows us to account for the fraction of Z < Zcrit stars formed even in regions in which the gas' average metallicity is well above Zcrit. We demonstrate that such partially-mixed regions account for 0.5 to 0.7 of all Pop III stars formed up to z = 5. Additionally, we track the creation and transport of "primordial metals" (PM) generated by Pop III supernovae (SNe). These neutron-capture deficient metals are taken up by second-generation stars and likely lead to unique abundance signatures characteristic of carbon-enhanced, metal-poor (CEMP-no) stars. As an illustrative example, we associate primordial metals with abundance ratios used by Keller et al. to explain the source of metals in the star SMSS J031300.36-670839.3, findin

preprint2016arXiv

Padé approximant for the equation of motion of a supernova remnant

In this paper we derive three equations of motion for a supernova remnant (SNR) in the framework of the thin layer approximation using the Padé approximant. The circumstellar medium is assumed to follow a density profile of either an exponential type, a Gaussian type, or a Lane--Emden ($n=5$) type. The three equations of motion are applied to four SNRs: Tycho, Cas A, Cygnus loop, and SN~1006. The percentage error of the Padé approximated solution is always less than $10\%$. The theoretical decrease of the velocity over ten years for SNRs is evaluated.

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