Culturally and Linguistically Responsive Noticing and Wondering: An Equity-Inducing yet Accessible Teaching Practice

Noticing and Wondering is a promising practice with an emerging research base in mathematics education for helping move teachers to a more contemporary paradigm of learning where culturally and linguistically diverse students have more equitable opportunities for academic success. This paper documents and extends this emerging research of Noticing and Wondering to fill a gap in the literature by (1) conceptualizing six reasons for the value of Noticing and Wondering and (2) discussing its potential to support English learners, such as by providing teachers easy access to students’ cultural assets. We document application of Noticing and Wondering beyond mathematics and conclude with a call for empirical research and practice in this direction

Line intensity enhancements in stellar coronal X-ray spectra due to opacity effects

Context. The I(15.01 A)/I(16.78 A) emission line intensity ratio in Fe XVII has been reported to deviate from its theoretical value in solar and stellar X-ray spectra. This is attributed to opacity in the 15.01 A line, leading to a reduction in its intensity, and was interpreted in terms of a geometry in which the emitters and absorbers are spatially distinct. Aims. We study the I(15.01 A)/I(16.78 A) intensity ratio for the active cool dwarf EV Lac, in both flare and quiescent spectra. Methods. The observations were obtained with the Reflection Grating Spectrometer on the XMM-Newton satellite. The emission measure distribution versus temperature reconstruction technique is used for our analysis. Results. We find that the 15.01 A line exhibits a significant enhancement in intensity over the optically thin value. To our knowledge, this is the first time that such an enhancement has been detected on such a sound statistical basis. We interpret this enhancement in terms of a geometry in which the emitters and absorbers are not spatially distinct, and where the geometry is such that resonant pumping of the upper level has a greater effect on the observed line intensity than resonant absorption in the line-of-sight.Comment: accepted for publication in A&

A re-analysis of the NuSTAR and XMM-Newton broad-band spectrum of Ser~X-1

Context: Ser X-1 is a well studied LMXB which clearly shows a broad iron line. Recently, Miller et al. (2103) have presented broad-band, high quality NuSTAR data of SerX-1.Using relativistically smeared self-consistent reflection models, they find a value of R_in close to 1.0 R_ISCO (corresponding to 6 R_g), and a low inclination angle, less than 10 deg. Aims: The aim of this paper is to probe to what extent the choice of reflection and continuum models (and uncertainties therein) can affect the conclusions about the disk parameters inferred from the reflection component. To this aim we re-analyze all the available public NuSTAR and XMM-Newton. Ser X-1 is a well studied source, its spectrum has been observed by several instruments, and is therefore one of the best sources for this study. Methods: We use slightly different continuum and reflection models with respect to those adopted in literature for this source. In particular we fit the iron line and other reflection features with self-consistent reflection models as reflionx (with a power-law illuminating continuum modified with a high energy cutoff to mimic the shape of the incident Comptonization spectrum) and rfxconv. With these models we fit NuSTAR and XMM-Newton spectra yielding consistent spectral results. Results: Our results are in line with those already found by Miller et al. (2013) but less extreme. In particular, we find the inner disk radius at about 13 R_g and an inclination angle with respect to the line of sight of about 27 deg. We conclude that, while the choice of the reflection model has little impact on the disk parameters, as soon as a self-consistent model is used, the choice of the continuum model can be important in the precise determination of the disk parameters from the reflection component. Hence broad-band X-ray spectra are highly preferable to constrain the continuum and disk parameters.Comment: 13 pages including 8 figures. Accepted for publication in A&

Updating the orbital ephemeris of the dipping source XB 1254-690 and the distance to the source

XB 1254-690 is a dipping low mass X-ray binary system hosting a neutron star and showing type I X-ray bursts. We aim at obtaining more accurate orbital ephemeris and at constraining the orbital period derivative of the system for the first time. In addition, we want to better constrain the distance to the source in order to locate the system in a well defined evolutive scenario. We apply for the first time an orbital timing technique to XB 1254-690, using the arrival times of the dips present in the light curves that have been collected during 26 years of X-ray pointed observations performed from different space missions. We estimate the dip arrival times using a statistical method that weights the count-rate inside the dip with respect to the level of the persistent emission outside the dip. We fit the obtained delays as a function of the orbital cycles both with a linear and a quadratic function. We infer the orbital ephemeris of XB 1254-690 improving the accuracy of the orbital period with respect to previous estimates. We infer a mass of M$_{2}=0.42\pm 0.04$ M$_{\odot}$ for the donor star, in agreement with the estimations already present in literature, assuming that the star is in thermal equilibrium while it transfers part of its mass via the inner Lagrangian point, and assuming a neutron star mass of 1.4 M$_{\odot}$. Using these assumptions, we also constrain the distance to the source, finding a value of 7.6$\pm 0.8$ kpc. Finally, we discuss the evolution of the system suggesting that it is compatible with a conservative mass transfer driven by magnetic braking.Comment: 13 pages, 5 figures, accepted for publication in Research in Astronomy and Astrophysics (RAA

Evidence of a non-conservative mass transfer for XTE J0929-314

Context. In 1998 the first accreting millisecond pulsar, SAX J1808.4-3658, was discovered and to date 18 systems showing coherent, high frequency (> 100 Hz) pulsations in low mass X-ray binaries are known. Since their discovery, this class of sources has shown interesting and sometimes puzzling behaviours. In particular, apart from a few exceptions, they are all transient with very long X-ray quiescent periods implying a quite low averaged mass accretion rate onto the neutron star. Among these sources, XTE J0929-314 has been detected in outburst just once in about 15 years of continuous monitoring of the X-ray sky. Aims. We aim to demonstrate that a conservative mass transfer in this system will result in an X-ray luminosity that is higher than the observed, long-term averaged X-ray luminosity. Methods. Under the hypothesis of a conservative mass transfer driven by gravitational radiation, as expected for this system given the short orbital period of about 43.6 min and the low mass of the companion implied by the mass function derived from timing techniques, we calculate the expected mass transfer rate in this system and predict the long-term averaged X-ray luminosity. This is compared with the averaged, over 15 years, X-ray flux observed from the system, and a lower limit of the distance to the source is inferred. Results. This distance is shown to be > 7.4 kpc in the direction of the Galactic anticentre, implying a large height, > 1.8 kpc, of the source with respect to the Galactic plane, placing the source in an empty region of the Galaxy. We suggest that the inferred value of the distance is unlikely. (abridged)Comment: 6 pages, 2 figures, accepted for publication in Astronomy & Astrophysics (A&A

New orbital ephemerides for the dipping source 4U 1323-619: constraining the distance to the source

4U 1323-619 is a low mass X-ray binary system that shows type I X-ray bursts and dips. The most accurate estimation of the orbital period is 2.941923(36) hrs and a distance from the source that is lower than 11 kpc has been proposed. We aim to obtain the orbital ephemeris, the orbital period of the system, as well as its derivative to compare the observed luminosity with that predicted by the theory of secular evolution. We took the advantage of about 26 years of X-ray data and grouped the selected observations when close in time. We folded the light curves and used the timing technique, obtaining 12 dip arrival times. We fit the delays of the dip arrival times both with a linear and a quadratic function. We locate 4U 1323-619 within a circular area centred at RA (J2000)= 201.6543\degree and DEC (J2000)= -62.1358\degree with an associated error of 0.0002\degree, and confirm the detection of the IR counterpart already discussed in literature. We estimate an orbital period of P=2.9419156(6) hrs compatible with the estimations that are present in the literature, but with an accuracy ten times higher. We also obtain a constraint on the orbital period derivative for the first time, estimating $\dot{P}=(8\pm 13)\times 10^{-12}$ s/s. Assuming that the companion star is in thermal equilibrium in the lower main sequence, and is a neutron star of 1.4 M$_{\odot}$, we infer a mass of 0.28$\pm$0.03 M$_{\odot}$ for the companion star. Assuming a distance of 10 kpc, we obtained a luminosity of (4.3$\pm$0.5)$\times 10^{36}$ erg s$^{-1}$, which is not in agreement with what is predicted by the theory of secular evolution. Using a 3D extinction map of the K$_{s}$ radiation in our Galaxy, we obtain a distance of 4.2$^{+0.8}_{-0.7}$ kpc at 68\% confidence level. (Abridged)Comment: 10 pages, 8 figures, accepted for publication in Astronomy & Astrophysic

A possible solution of the puzzling variation of the orbital period of MXB 1659-298

MXB 1659-298 is a transient neutron star Low-Mass X-ray binary system that shows eclipses with a periodicity of 7.1 hr. The source went to outburst in August 2015 after 14 years of quiescence. We investigate the orbital properties of this source with a baseline of 40 years obtained combining the eight eclipse arrival times present in literature with 51 eclipse arrival times collected during the last two outbursts. A quadratic ephemeris does not fit the delays associated with the eclipse arrival times and the addition of a sinusoidal term with a period of $2.31 \pm 0.02$ yr is required. We infer a binary orbital period of $P=7.1161099(3)$ hr and an orbital period derivative of $\dot{P}=-8.5(1.2) \times 10^{-12}$ s s$^{-1}$. We show that the large orbital period derivative can be explained with a highly non conservative mass transfer scenario in which more than 98\% of the mass provided by the companion star leaves the binary system. We predict an orbital period derivative value of $\dot{P}=-6(3) \times 10^{-12}$ s s$^{-1}$ and constrain the companion star mass between $\sim$0.3 and $0.9 \pm 0.3$ M$_{\odot}$. Assuming that the companion star is in thermal equilibrium the periodic modulation can be due to either a gravitational quadrupole coupling due to variations of the oblateness of the companion star or with the presence of a third body of mass M$_3 >21$ Jovian masses.Comment: 10 pages, 6 figures. Accepted by MNRA

Study of the reflection spectrum of the LMXB 4U 1702-429

The source 4U 1702-429 (Ara X-1) is a low-mass X-ray binary system hosting a neutron star. Albeit the source is quite bright ( $\sim10^{37}$ erg s$^{-1}$) its broadband spectrum has never been studied. Neither dips nor eclipses have been observed in the light curve suggesting that its inclination angle is smaller than 60$^{\circ}$.We analysed the broadband spectrum of 4U 1702-429 in the 0.3-60 keV energy range, using XMM-Newton and INTEGRAL data, to constrain its Compton reflection component if it is present. After excluding the three time intervals in which three type-I X-ray bursts occurred, we fitted the joint XMM-Newton and INTEGRAL spectra obtained from simultaneous observations. A broad emission line at 6.7 keV and two absorption edges at 0.87 and 8.82 keV were detected. We found that a self-consistent reflection model fits the 0.3-60 keV spectrum well. The broadband continuum is composed of an emission component originating from the inner region of the accretion disc, a Comptonised direct emission coming from a corona with an electron temperature of $2.63 \pm 0.06$ keV and an optical depth $\tau=13.6 \pm 0.2$, and, finally, a reflection component. The best-fit indicates that the broad emission line and the absorption edge at 8.82 keV, both associated with the presence of \ion{Fe}{xxv} ions, are produced by reflection in the region above the disc with a ionisation parameter of $Log(\xi) \simeq 2.7$. We have inferred that the inner radius, where the broad emission line originates, is $64^{+52}_{-15}$ km, and the inner radius of the accretion disc is $39^{+6}_{-8}$ km. (Abridged)Comment: 9 pages, 9 figures, accepted for publication by A&

Detection of vitellogenin in a subpopulation of sea urchin coelomocytes

Sea urchin vitellogenin is a high molecular weight glycoprotein, which is the precursor of the major yolk protein present in the unfertilized egg. Vitellogenin processing into the major yolk protein and its further enzymatic cleavage during sea urchin embryonic development, has been extensively described, and the adhesive properties of the processed molecule have been studied. The function of vitellogenin in the adult, where it has been found in the coelomic fluid of both male and female individuals, is still unknown, although its role on promoting the adhesion of embryonic cells has been shown. In this report we describe the detection of vitellogenin in lysates of whole circulating coelomocytes of both male and female sea urchins of the species Paracentrotus lividus. By metrizoic acid gradients we purified total coelomocytes into six subpopulations that were tested for the occurrence of the molecule using vitellogenin-specific polyclonal antibodies. We detected vitellogenin only in the coelomocyte subpopulation called colorless spherule cells, packed in kidney-shaped granules located around the nucleus. We also showed that coelomocytes respond to stress conditions by discharging vitellogenin into the medium. This result together with previous observations on the adhesive properties of the molecule suggest a role for vitellogenin in the clotting phenomenon occurring after host invasion