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D. Dominis Prester

Publications and source records attributed to D. Dominis Prester.

At least 163 records · Page 9Linked to original sources

Rapid and multi-band variability of the TeV-bright active nucleus of the galaxy IC 310

Context. The radio galaxy IC 310 has recently been identified as a gamma-ray emitter based on observations at GeV energies with Fermi-LAT and at very high energies (VHE, E>100GeV) with the MAGIC telescopes. Originally classified as a head-tail radio galaxy, the nature of this object is subject of controversy since its nucleus shows blazar-like behavior. Aims. In order to understand the nature of IC 310 and the origin of the VHE emission we studied the spectral and flux variability of IC 310 from the X-ray band to the VHE gamma-ray regime. Methods. The light curve of IC 310 above 300GeV has been measured with the MAGIC telescopes from Oct. 2009 to Feb. 2010. Fermi-LAT data (2008-2011) in the 10-500GeV energy range were also analyzed. In X-ray, archival observations from 2003 to 2007 with XMM, Chandra, and Swift-XRT in the 0.5-10keV band were studied. Results. The VHE light curve reveals several high-amplitude and short-duration flares. Day-to-day flux variability is clearly present. The photon index between 120GeV and 8TeV remains at the value $Γ\sim2.0$ during both low and high flux states. The VHE spectral shape does not show significant variability, whereas the flux at 1TeV changes by a factor of $\sim7$. Fermi-LAT detected only eight gamma-ray events in the energy range 10GeV-500GeV in three years of observation. The measured photon index of $Γ=1.3\pm0.5$ in the Fermi-LAT range is very hard. The X-ray measurements show strong variability in flux and photon index. The latter varied from $1.76\pm0.07$ to $2.55\pm0.07$. Conclusion. The rapid variability measured confirms the blazar-like behavior of IC 310. The TeV emission seems to originate from scales of less than 80 Schwarzschild radii within the compact core of its FRI radio jet with orientation angle 10deg-38deg. The SED resembles that of an extreme blazar, albeit the luminosity is more than two orders of magnitude lower.

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A Sub-Earth-Mass Moon Orbiting a Gas Giant Primary or a High Velocity Planetary System in the Galactic Bulge

We present the first microlensing candidate for a free-floating exoplanet-exomoon system, MOA-2011-BLG-262, with a primary lens mass of M_host ~ 4 Jupiter masses hosting a sub-Earth mass moon. The data are well fit by this exomoon model, but an alternate star+planet model fits the data almost as well. Nevertheless, these results indicate the potential of microlensing to detect exomoons, albeit ones that are different from the giant planet moons in our solar system. The argument for an exomoon hinges on the system being relatively close to the Sun. The data constrain the product M pi_rel, where M is the lens system mass and pi_rel is the lens-source relative parallax. If the lens system is nearby (large pi_rel), then M is small (a few Jupiter masses) and the companion is a sub-Earth-mass exomoon. The best-fit solution has a large lens-source relative proper motion, mu_rel = 19.6 +- 1.6 mas/yr, which would rule out a distant lens system unless the source star has an unusually high proper motion. However, data from the OGLE collaboration nearly rule out a high source proper motion, so the exoplanet+exomoon model is the favored interpretation for the best fit model. However, the alternate solution has a lower proper motion, which is compatible with a distant (so stellar) host. A Bayesian analysis does not favor the exoplanet+exomoon interpretation, so Occam's razor favors a lens system in the bulge with host and companion masses of M_host = 0.12 (+0.19 -0.06) M_solar and m_comp = 18 (+28 -100 M_earth, at a projected separation of a_perp ~ 0.84 AU. The existence of this degeneracy is an unlucky accident, so current microlensing experiments are in principle sensitive to exomoons. In some circumstances, it will be possible to definitively establish the low mass of such lens systems through the microlensing parallax effect. Future experiments will be sensitive to less extreme exomoons.

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A Super-Jupiter orbiting a late-type star: A refined analysis of microlensing event OGLE-2012-BLG-0406

We present a detailed analysis of survey and follow-up observations of microlensing event OGLE-2012-BLG-0406 based on data obtained from 10 different observatories. Intensive coverage of the lightcurve, especially the perturbation part, allowed us to accurately measure the parallax effect and lens orbital motion. Combining our measurement of the lens parallax with the angular Einstein radius determined from finite-source effects, we estimate the physical parameters of the lens system. We find that the event was caused by a $2.73\pm 0.43\ M_{\rm J}$ planet orbiting a $0.44\pm 0.07\ M_{\odot}$ early M-type star. The distance to the lens is $4.97\pm 0.29$\ kpc and the projected separation between the host star and its planet at the time of the event is $3.45\pm 0.26$ AU. We find that the additional coverage provided by follow-up observations, especially during the planetary perturbation, leads to a more accurate determination of the physical parameters of the lens.

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MAGIC upper limits on the GRB 090102 afterglow

Indications of a GeV component in the emission from GRBs are known since the EGRET observations during the 1990's and they have been confirmed by the data of the Fermi satellite. These results have, however, shown that our understanding of GRB physics is still unsatisfactory. The new generation of Cherenkov observatories and in particular the MAGIC telescope, allow for the first time the possibility to extend the measurement of GRBs from several tens up to hundreds of GeV energy range. Both leptonic and hadronic processes have been suggested to explain the possible GeV/TeV counterpart of GRBs. Observations with ground-based telescopes of very high energy photons (E>30 GeV) from these sources are going to play a key role in discriminating among the different proposed emission mechanisms, which are barely distinguishable at lower energies. MAGIC telescope observations of the GRB 090102 (z=1.547) field and Fermi Large Area Telescope (LAT) data in the same time interval are analysed to derive upper limits of the GeV/TeV emission. We compare these results to the expected emissions evaluated for different processes in the framework of a relativistic blast wave model for the afterglow. Simultaneous upper limits with Fermi and a Cherenkov telescope have been derived for this GRB observation. The results we obtained are compatible with the expected emission although the difficulties in predicting the HE and VHE emission for the afterglow of this event makes it difficult to draw firmer conclusions. Nonetheless, MAGIC sensitivity in the energy range of overlap with space-based instruments (above about 40 GeV) is about one order of magnitude better with respect to Fermi. This makes evident the constraining power of ground-based observations and shows that the MAGIC telescope has reached the required performance to make possible GRB multiwavelength studies in the very high energy range.

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MOA-2010-BLG-311: A planetary candidate below the threshold of reliable detection

We analyze MOA-2010-BLG-311, a high magnification (A_max>600) microlensing event with complete data coverage over the peak, making it very sensitive to planetary signals. We fit this event with both a point lens and a 2-body lens model and find that the 2-body lens model is a better fit but with only Delta chi^2~80. The preferred mass ratio between the lens star and its companion is $q=10^(-3.7+/-0.1), placing the candidate companion in the planetary regime. Despite the formal significance of the planet, we show that because of systematics in the data the evidence for a planetary companion to the lens is too tenuous to claim a secure detection. When combined with analyses of other high-magnification events, this event helps empirically define the threshold for reliable planet detection in high-magnification events, which remains an open question.

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MOA-2010-BLG-328Lb: a sub-Neptune orbiting very late M dwarf ?

We analyze the planetary microlensing event MOA-2010-BLG-328. The best fit yields host and planetary masses of Mh = 0.11+/-0.01 M_{sun} and Mp = 9.2+/-2.2M_Earth, corresponding to a very late M dwarf and sub-Neptune-mass planet, respectively. The system lies at DL = 0.81 +/- 0.10 kpc with projected separation r = 0.92 +/- 0.16 AU. Because of the host's a-priori-unlikely close distance, as well as the unusual nature of the system, we consider the possibility that the microlens parallax signal, which determines the host mass and distance, is actually due to xallarap (source orbital motion) that is being misinterpreted as parallax. We show a result that favors the parallax solution, even given its close host distance. We show that future high-resolution astrometric measurements could decisively resolve the remaining ambiguity of these solutions.

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Interpretation of a Short-Term Anomaly in the Gravitational Microlensing Event MOA-2012-BLG-486

A planetary microlensing signal is generally characterized by a short-term perturbation to the standard single lensing light curve. A subset of binary-source events can produce perturbations that mimic planetary signals, thereby introducing an ambiguity between the planetary and binary-source interpretations. In this paper, we present analysis of the microlensing event MOA-2012-BLG-486, for which the light curve exhibits a short-lived perturbation. Routine modeling not considering data taken in different passbands yields a best-fit planetary model that is slightly preferred over the best-fit binary-source model. However, when allowed for a change in the color during the perturbation, we find that the binary-source model yields a significantly better fit and thus the degeneracy is clearly resolved. This event not only signifies the importance of considering various interpretations of short-term anomalies, but also demonstrates the importance of multi-band data for checking the possibility of false-positive planetary signals.

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The Simultaneous Low State Spectral Energy Distribution of 1ES 2344+514 from Radio to Very High Energies

[Abridged] Context. To construct and interpret the spectral energy distribution (SED) of BL Lacertae objects, simultaneous broad-band observations are mandatory. Aims. We present the results of a dedicated multi-wavelength study of the high-frequency peaked BL Lacertae (HBL) object and known TeV emitter 1ES 2344+514 by means of a pre-organised campaign. Methods. The observations were conducted during simultaneous visibility windows of MAGIC and AGILE in late 2008. The measurements were complemented by Metsähovi, RATAN-600, KVA+Tuorla, Swift and VLBA pointings. Additional coverage was provided by the ongoing long-term F-GAMMA and MOJAVE programs, the OVRO 40-m and CrAO telescopes as well as the Fermi satellite. The obtained SEDs are modelled using a one-zone as well as a self-consistent two-zone synchrotron self-Compton model. Results. 1ES 2344+514 was found at very low flux states in both X-rays and very high energy gamma rays. Variability was detected in the low frequency radio and X-ray bands only, where for the latter a small flare was observed. The X-ray flare was possibly caused by shock acceleration characterised by similar cooling and acceleration time scales. MOJAVE VLBA monitoring reveals a static jet whose components are stable over time scales of eleven years, contrary to previous findings. There appears to be no significant correlation between the 15 GHz and R-band monitoring light curves. The observations presented here constitute the first multi-wavelength campaign on 1ES 2344+514 from radio to VHE energies and one of the few simultaneous SEDs during low activity states. The quasi-simultaneous Fermi-LAT data poses some challenges for SED modelling, but in general the SEDs are described well by both applied models. The resulting parameters are typical for TeV emitting HBLs. Consequently it remains unclear whether a so-called quiescent state was found in this campaign.

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Discovery of very high energy gamma-ray emission from the blazar 1ES 1727+502 with the MAGIC Telescopes

Motivated by the Costamante & Ghisellini (2002) predictions we investigated if the blazar 1ES 1727+502 (z=0.055) is emitting very high energy (VHE, E>100 GeV) gamma rays. We observed the BL Lac object 1ES 1727+502 in stereoscopic mode with the two MAGIC telescopes during 14 nights between May 6th and June 10th 2011, for a total effective observing time of 12.6 hours. For the study of the multiwavelength spectral energy distribution (SED) we use simultaneous optical R-band data from the KVA telescope, archival UV/optical and X-ray observations by instruments UVOT and XRT on board of the Swift satellite and high energy (HE, 0.1 GeV - 100 GeV) gamma-ray data from the Fermi-LAT instrument. We detect, for the first time, VHE gamma-ray emission from 1ES 1727+502 at a statistical significance of 5.5 sigma. The integral flux above 150 GeV is estimated to be (2.1\pm0.4)% of the Crab Nebula flux and the de-absorbed VHE spectrum has a photon index of (2.7\pm0.5). No significant short-term variability was found in any of the wavebands presented here. We model the SED using a one-zone synchrotron self-Compton model obtaining parameters typical for this class of sources.

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MOA-2010-BLG-073L: An M-Dwarf with a Substellar Companion at the Planet/Brown Dwarf Boundary

We present an analysis of the anomalous microlensing event, MOA-2010-BLG-073, announced by the Microlensing Observations in Astrophysics survey on 2010-03-18. This event was remarkable because the source was previously known to be photometrically variable. Analyzing the pre-event source lightcurve, we demonstrate that it is an irregular variable over time scales >200d. Its dereddened color, $(V-I)_{S,0}$, is 1.221$\pm$0.051mag and from our lens model we derive a source radius of 14.7$\pm$1.3 $R_{\odot}$, suggesting that it is a red giant star. We initially explored a number of purely microlensing models for the event but found a residual gradient in the data taken prior to and after the event. This is likely to be due to the variability of the source rather than part of the lensing event, so we incorporated a slope parameter in our model in order to derive the true parameters of the lensing system. We find that the lensing system has a mass ratio of q=0.0654$\pm$0.0006. The Einstein crossing time of the event, $T_{\rm{E}}=44.3$\pm$0.1d, was sufficiently long that the lightcurve exhibited parallax effects. In addition, the source trajectory relative to the large caustic structure allowed the orbital motion of the lens system to be detected. Combining the parallax with the Einstein radius, we were able to derive the distance to the lens, $D_L$=2.8$\pm$0.4kpc, and the masses of the lensing objects. The primary of the lens is an M-dwarf with $M_{L,p}$=0.16$\pm0.03M_{\odot}$ while the companion has $M_{L,s}$=11.0$\pm2.0M_{\rm{J}}$ putting it in the boundary zone between planets and brown dwarfs.

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Observations of the magnetars 4U 0142+61 and 1E 2259+586 with the MAGIC telescopes

Magnetars are an extreme, highly magnetized class of isolated neutron stars whose large X-ray luminosity is believed to be driven by their high magnetic field. In this work we study for the first time the possible very high energy gamma-ray emission above 100 GeV from magnetars, observing the sources 4U 0142+61 and 1E 2259+586. We observed the two sources with atmospheric Cherenkov telescopes in the very high energy range (E > 100 GeV). 4U 0142+61 was observed with the MAGIC I telescope in 2008 for ~25 h and 1E 2259+586 was observed with the MAGIC stereoscopic system in 2010 for ~14 h. The data were analyzed with the standard MAGIC analysis software. Neither magnetar was detected. Upper limits to the differential and integral flux above 200 GeV were computed using the Rolke algorithm. We obtain integral upper limits to the flux of 1.52*10^-12cm^-2 s^-1 and 2.7*10^-12cm^-2 s^-1 with a confidence level of 95% for 4U 0142+61 and 1E 2259+586, respectively. The resulting differential upper limits are presented together with X-ray data and upper limits in the GeV energy range.

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Mrk 421 active state in 2008: the MAGIC view, simultaneous multi-wavelength observations and SSC model constrained

Context: The blazar Markarian 421 is one of the brightest TeV gamma-ray sources of the northern sky. From December 2007 until June 2008 it was intensively observed in the very high energy (VHE, E > 100 GeV) band by the single-dish Major Atmospheric Gamma-ray Imaging Cherenkov telescope (MAGIC-I). Aims: We aimed to measure the physical parameters of the emitting region of the blazar jet during active states. Methods: We performed a dense monitoring of the source in VHE with MAGIC-I, and also collected complementary data in soft X-rays and optical-UV bands; then, we modeled the spectral energy distributions (SED) derived from simultaneous multi-wavelength data within the synchrotron self--compton (SSC) framework. Results: The source showed intense and prolonged gamma-ray activity during the whole period, with integral fluxes (E > 200 GeV) seldom below the level of the Crab Nebula, and up to 3.6 times this value. Eight datasets of simultaneous optical-UV (KVA, Swift/UVOT), soft X-ray (Swift/XRT) and MAGIC-I VHE data were obtained during different outburst phases. The data constrain the physical parameters of the jet, once the spectral energy distributions obtained are interpreted within the framework of a single-zone SSC leptonic model. Conclusions: The main outcome of the study is that within the homogeneous model high Doppler factors (40 <= delta <= 80) are needed to reproduce the observed SED; but this model cannot explain the observed short time-scale variability, while it can be argued that inhomogeneous models could allow for less extreme Doppler factors, more intense magnetic fields and shorter electron cooling times compatible with hour or sub-hour scale variability.

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Discovery of VHE gamma-rays from the blazar 1ES 1215+303 with the MAGIC Telescopes and simultaneous multi-wavelength observations

Context. We present the discovery of very high energy (VHE, E > 100GeV) gamma-ray emission from the BL Lac object 1ES 1215+303 by the MAGIC telescopes and simultaneous multi-wavelength data in a broad energy range from radio to gamma-rays. Aims. We study the VHE gamma-ray emission from 1ES 1215+303 and its relation to the emissions in other wavelengths. Methods. Triggered by an optical outburst, MAGIC observed the source in January-February 2011 for 20.3 hrs. The target was monitored in the optical R-band by the KVA telescope that also performed optical polarization measurements. We triggered target of opportunity observations with the Swift satellite and obtained simultaneous and quasi-simultaneous data from the Fermi Large Area Telescope and from the Metsähovi radio telescope. We also present the analysis of older MAGIC data taken in 2010. Results. The MAGIC observations of 1ES 1215+303 carried out in January-February 2011 resulted in the first detection of the source at VHE with a statistical significance of 9.4 sigma. Simultaneously, the source was observed in a high optical and X-ray state. In 2010 the source was observed in a lower state in optical, X-ray, and VHE, while the GeV gamma-ray flux and the radio flux were comparable in 2010 and 2011. The spectral energy distribution obtained with the 2011 data can be modeled with a simple one zone SSC model, but it requires extreme values for the Doppler factor or the electron energy distribution.

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MAGIC observations of the giant radio galaxy M87 in a low-emission state between 2005 and 2007

We present the results of a long M87 monitoring campaign in very high energy $γ$-rays with the MAGIC-I Cherenkov telescope. We aim to model the persistent non-thermal jet emission by monitoring and characterizing the very high energy $γ$-ray emission of M87 during a low state. A total of 150\,h of data were taken between 2005 and 2007 with the single MAGIC-I telescope, out of which 128.6\,h survived the data quality selection. We also collected data in the X-ray and \textit{Fermi}--LAT bands from the literature (partially contemporaneous). No flaring activity was found during the campaign. The source was found to be in a persistent low-emission state, which was at a confidence level of $7σ$. We present the spectrum between 100\,GeV and 2\,TeV, which is consistent with a simple power law with a photon index $Γ=2.21\pm0.21$ and a flux normalization at 300\,GeV of $(7.7\pm1.3) \times 10^{-8}$ TeV$^{-1}$ s$^{-1}$ m$^{-2}$. The extrapolation of the MAGIC spectrum into the GeV energy range matches the previously published \textit{Fermi}--LAT spectrum well, covering a combined energy range of four orders of magnitude with the same spectral index. We model the broad band energy spectrum with a spine layer model, which can satisfactorily describe our data.

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High zenith angle observations of PKS 2155-304 with the MAGIC-I telescope

The high frequency peaked BL Lac PKS 2155-304 with a redshift of z=0.116 was discovered in 1997 in the very high energy (VHE, E >100GeV) gamma-ray range by the University of Durham Mark VI gamma-ray Cherenkov telescope in Australia with a flux corresponding to 20% of the Crab Nebula flux. It was later observed and detected with high significance by the Southern Cherenkov observatory H.E.S.S. Detection from the Northern hemisphere is difficult due to challenging observation conditions under large zenith angles. In July 2006, the H.E.S.S. collaboration reported an extraordinary outburst of VHE gamma-emission. During the outburst, the VHE gamma-ray emission was found to be variable on the time scales of minutes and with a mean flux of ~7 times the flux observed from the Crab Nebula. Follow-up observations with the MAGIC-I standalone Cherenkov telescope were triggered by this extraordinary outburst and PKS 2155-304 was observed between 28 July to 2 August 2006 for 15 hours at large zenith angles. Here we present our studies on the behavior of the source after its extraordinary flare and an enhanced analysis method for data taken at high zenith angles. We developed improved methods for event selection that led to a better background suppression. The averaged energy spectrum we derived has a spectral index of -3.5 +/- 0.2 above 400GeV, which is in good agreement with the spectral shape measured by H.E.S.S. during the major flare on MJD 53944. Furthermore, we present the spectral energy distribution modeling of PKS 2155-304. With our observations we increased the duty cycle of the source extending the light curve derived by H.E.S.S. after the outburst. Finally, we find night-by-night variability with a maximal amplitude of a factor three to four and an intranight variability in one of the nights (MJD 53945) with a similar amplitude.

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A possible binary system of a stellar remnant in the high magnification gravitational microlensing event OGLE-2007-BLG-514

We report the extremely high magnification (A > 1000) binary microlensing event OGLE-2007-BLG-514. We obtained good coverage around the double peak structure in the light curve via follow-up observations from different observatories. The binary lens model that includes the effects of parallax (known orbital motion of the Earth) and orbital motion of the lens yields a binary lens mass ratio of q = 0.321 +/- 0.007 and a projected separation of s = 0.072 +/- 0.001$ in units of the Einstein radius. The parallax parameters allow us to determine the lens distance D_L = 3.11 +/- 0.39 kpc and total mass M_L=1.40 +/- 0.18 M_sun; this leads to the primary and secondary components having masses of M_1 = 1.06 +/- 0.13 M_sun and M_2 = 0.34 +/- 0.04 M_sun, respectively. The parallax model indicates that the binary lens system is likely constructed by the main sequence stars. On the other hand, we used a Bayesian analysis to estimate probability distributions by the model that includes the effects of xallarap (possible orbital motion of the source around a companion) and parallax (q = 0.270 +/- 0.005, s = 0.083 +/- 0.001). The primary component of the binary lens is relatively massive with M_1 = 0.9_{-0.3}^{+4.6} M_sun and it is at a distance of D_L = 2.6_{-0.9}^{+3.8} kpc. Given the secure mass ratio measurement, the companion mass is therefore M_2 = 0.2_{-0.1}^{+1.2} M_sun. The xallarap model implies that the primary lens is likely a stellar remnant, such as a white dwarf, a neutron star or a black hole.

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MOA-2010-BLG-477Lb: constraining the mass of a microlensing planet from microlensing parallax, orbital motion and detection of blended light

Microlensing detections of cool planets are important for the construction of an unbiased sample to estimate the frequency of planets beyond the snow line, which is where giant planets are thought to form according to the core accretion theory of planet formation. In this paper, we report the discovery of a giant planet detected from the analysis of the light curve of a high-magnification microlensing event MOA-2010-BLG-477. The measured planet-star mass ratio is $q=(2.181\pm0.004)\times 10^{-3}$ and the projected separation is $s=1.1228\pm0.0006$ in units of the Einstein radius. The angular Einstein radius is unusually large $θ_{\rm E}=1.38\pm 0.11$ mas. Combining this measurement with constraints on the "microlens parallax" and the lens flux, we can only limit the host mass to the range $0.13<M/M_\odot<1.0$. In this particular case, the strong degeneracy between microlensing parallax and planet orbital motion prevents us from measuring more accurate host and planet masses. However, we find that adding Bayesian priors from two effects (Galactic model and Keplerian orbit) each independently favors the upper end of this mass range, yielding star and planet masses of $M_*=0.67^{+0.33}_{-0.13}\ M_\odot$ and $m_p=1.5^{+0.8}_{-0.3}\ M_{\rm JUP}$ at a distance of $D=2.3\pm0.6$ kpc, and with a semi-major axis of $a=2^{+3}_{-1}$ AU. Finally, we show that the lens mass can be determined from future high-resolution near-IR adaptive optics observations independently from two effects, photometric and astrometric.

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Constraining Cosmic Rays and Magnetic Fields in the Perseus Galaxy Cluster with TeV observations by the MAGIC telescopes

Galaxy clusters are being assembled today in the most energetic phase of hierarchical structure formation which manifests itself in powerful shocks that contribute to a substantial energy density of cosmic rays (CRs). Hence, clusters are expected to be luminous gamma-ray emitters since they also act as energy reservoirs for additional CR sources, such as active galactic nuclei and supernova-driven galactic winds. To detect the gamma-ray emission from CR interactions with the ambient cluster gas, we conducted the deepest to date observational campaign targeting a galaxy cluster at very high-energy gamma-rays and observed the Perseus cluster with the MAGIC Cherenkov telescopes for a total of ~85 hr of effective observing time. This campaign resulted in the detection of the central radio galaxy NGC 1275 at energies E > 100 GeV with a very steep energy spectrum. Here, we restrict our analysis to energies E > 630 GeV and detect no significant gamma-ray excess. This constrains the average CR-to-thermal pressure ratio to be <= 1-2%, depending on assumptions and the model for CR emission. Comparing these gamma-ray upper limits to predictions from cosmological cluster simulations that include CRs constrains the maximum CR acceleration efficiency at structure formation shocks to be < 50%. Alternatively, this may argue for non-negligible CR transport processes such as CR streaming and diffusion into the outer cluster regions. Finally, we derive lower limits on the magnetic field distribution assuming that the Perseus radio mini-halo is generated by secondary electrons/positrons that are created in hadronic CR interactions: assuming a spectrum of E^-2.2 around TeV energies as implied by cluster simulations, we limit the central magnetic field to be > 4-9 microG, depending on the rate of decline of the magnetic field strength toward larger radii.

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