Discovery of the variable optical counterpart of the redback pulsar PSR J2055+1545

ABSTRACT

We present the discovery of the variable optical counterpart to PSR J2055|$+$|1545, a redback millisecond pulsar, and the first radial velocity curve of its companion star. The multiband optical light curves of this system show a 0.4–|$0.6 \ \mathrm{mag}$| amplitude modulation with a single peak per orbit and variable colours, suggesting that the companion is mildly irradiated by the pulsar wind. We find that the flux maximum is asymmetric and occurs at orbital phase |$\simeq 0.4$|⁠, anticipating the superior conjunction of the companion (where the optical emission of irradiated redback companions is typically brightest). We ascribe this asymmetry, well fit with a hotspot in our light-curve modelling, to irradiation from the intrabinary shock between pulsar and companion winds. The optical spectra obtained with the Gran Telescopio Canarias reveal a G-dwarf companion star with temperatures of |$5749 \pm 34 \ \mathrm{K}$| and |$6106 \pm 35 \ \mathrm{K}$| at its inferior and superior orbital conjunctions, respectively, and a radial velocity semi-amplitude of |$385 \pm 3 {\mathrm{\, km\, s^{-1}}}{}$|⁠. Our best-fitting model yields a neutron star mass of |$1.7^{+0.4}_{-0.1} \ \mathrm{M}_{\odot }$| and a companion mass of |$0.29^{+0.07}_{-0.01} \ \mathrm{M}_{\odot }$|⁠. Based on the close similarity between the optical light curve of PSR J2055|$+$|1545 and those observed from PSR J1023|$+$|0038 and PSR J1227–4853 during their rotation-powered states, we suggest this system may develop an accretion disc in the future and manifest as a transitional millisecond pulsar.

1 INTRODUCTION

Millisecond pulsars (MSPs) are rapidly rotating neutron stars that originate from low-mass X-ray binary (LMXB) progenitor systems. During this LMXB phase, the companion star transfers matter and angular momentum to the neutron star, spinning it up to |$\sim \mathrm{ms}$| periods (Radhakrishnan & Srinivasan 1982). Once the outward pressure exerted by the neutron star’s magnetic field exceeds the inward ram pressure of the accreting material, the accretion disc is expelled, allowing the neutron star to become active as a rotation-powered radio MSP (Tauris et al. 2013).

Spiders are a subclass of MSPs found in compact binary systems (⁠|$P_{\mathrm{orb}}\lesssim 1 \ \mathrm{d}$|⁠), where the pulsar’s high-energy particle wind can irradiate and progressively consume their companion stars, potentially fully devouring them in few cases (Fruchter, Stinebring & Taylor 1988; van den Heuvel & van Paradijs 1988). This extreme interaction has earned these systems the nicknames black widows (BWs) and redbacks (RBs), characterized by companion masses |$M_{2}\sim 0.01 \ \mathrm{M}_{\odot }$| and |$M_{2}\simeq 0.3$|–|$0.7 \ \mathrm{M}_{\odot }$|⁠, respectively. Notably, three transitional MSPs within the RB category have been observed switching between the accretion-powered disc state and the radio pulsar state over time-scales of a few weeks to months (Archibald et al. 2009; Papitto et al. 2013; Bassa et al. 2014), positioning RBs as the missing link between the LMXB and MSP evolutionary phases. Furthermore, spider binaries in general are considered prime systems for hosting supermassive neutron stars, having undergone prolonged Gyr-long accretion episodes before activating as radio MSPs (Linares 2020).

Spider MSPs often show large eclipses of their radio pulsations, caused by absorption from material expelled by the companion star (Polzin et al. 2020), making their detection in blind radio surveys particularly challenging. Over the past 16 yr, the Fermi Large Area Telescope (Fermi-LAT; Abdollahi et al. 2020) has played a crucial role in expanding the known spider population, with 65 confirmed systems to date (Nedreaas 2024). Since its launch, Fermi has enabled the discovery of numerous spider MSPs, not only as |$\gamma$|-ray emitters (Smith et al. 2023), but also through targeted radio searches of previously unassociated |$\gamma$|-ray sources (Thongmeearkom et al. 2024).

Spider systems can also be identified through the variable optical emission of their companion stars (e.g. Salvetti et al. 2015; Linares et al. 2017; Au et al. 2023). The shape of their light curves is primarily determined by the degree of heating from the pulsar wind, which in turn depends on the system’s orbital period, the companion star’s intrinsic ‘base’ temperature and the pulsar’s spin-down luminosity (Turchetta et al. 2023). Indeed, all currently known BWs exhibit irradiation-dominated optical light curves, with peak-to-peak amplitudes |$\gtrsim 1 \ \mathrm{mag}$| and a single flux maximum per orbit, owing to their relatively cold companion stars (⁠|$\simeq 1000$|–|$3000 \ \mathrm{K}$|⁠). On the other hand RB companions are hotter (⁠|$\simeq 4000$|–|$6000 \ \mathrm{K}$|⁠), thus about half of them show little to no irradiation effects, resulting in double-peaked light curves with amplitudes |$\simeq 0.3 \ \mathrm{mag}$| driven by the tidal distortion of the companion. Combining optical light-curve modelling with independent spectroscopic measurements of the companion’s radial velocity is crucial for obtaining precise and robust constraints on the fundamental parameters of spider systems, particularly their neutron star masses (e.g. Linares, Shahbaz & Casares 2018; Romani et al. 2021; Dodge et al. 2024).

PSR J2055|$+$|1545 (hereafter referred to as J2055) is a RB system discovered as a radio MSP by Lewis et al. (2023), with a spin period of |$2.16 \ \mathrm{ms}$| and an orbital period of |$4.8 \ \mathrm{hr}$|⁠. It has been classified as a RB MSP based on the observed radio eclipse, spanning 36 per cent of its orbit, and an estimated median companion mass of |$0.29 \ \mathrm{M}_{\odot }$| (Lewis et al. 2023). Additionally, J2055 is associated with the pulsar-like Fermi source 4FGL J2055.8|$+$|1545, although no |$\gamma$|-ray pulsations have been detected. This is likely due to the system’s substantial orbital variability, which makes it difficult to maintain phase coherence outside the time range covered by the radio ephemeris. Optical counterparts to J2055 have been identified in Gaia Data Release 3 (DR3; Gaia Collaboration 2023), Pan-STARRS 1 (PS1; Chambers et al. 2016), and Sloan Digital Sky Survey Data Release 17 (SDSS-DR17; Abdurro’uf et al. 2022), no optical photometric or spectroscopic observations have yet been performed. Consequently, key parameters such as the neutron star mass, orbital inclination, and companion temperature remain either unknown or poorly constrained.

In this paper, we present the discovery of the variable optical counterpart of J2055 and the first radial velocity curve for this system. Section 2 details the two optical campaigns conducted in 2023 and 2024, along with the photometric and spectral analysis techniques employed. In Section 3, we report the optical light curves of J2055, which exhibit a single asymmetric flux maximum per orbit, indicative of an irradiated companion, as well as the system’s radial velocity curve. Section 4 focuses on the combined modelling of the 2023 and 2024 light curves using the Icarus software (Breton et al. 2012), where we use the semi-amplitude of the companion’s radial velocity, derived from spectroscopy, as the central value for its prior distribution. In Section 5, we interpret and discuss our findings, comparing the key optical features and the intermediate irradiated regime observed in J2055 with those of other RB systems.

2 OBSERVATIONS AND DATA ANALYSIS

2.1 Photometry

We carried out an optical photometric campaign of J2055 spanning 1 yr, from 2023 July to 2024 August. The 2023 observations were obtained using the Sinistro and ALFOSC cameras mounted on the 1-|$\mathrm{m}$| LCO and 2.56-|$\mathrm{m}$| NOT telescopes, respectively, while the 2024 data were exclusively acquired with the NOT/ALFOSC set-up. The observations consisted of 5-min long exposures, alternating between the SDSS g’, r’, and i’ filters. Instrumental set-ups and additional details of these observations are provided in Table 1.

We processed the LCO and NOT data using the banzai data-reduction pipeline¹ and the standard tools of iraf (v. 2.16, Tody 1986), respectively. The photometric techniques applied to the data were the same for LCO and NOT images. The analyses were performed separately on the 2023 LCO, 2023 NOT, and 2024 NOT data sets.

We combined the reduced images into a single median image for each of the three optical bands, g’, r’, and i’, to enhance the source detection sensitivity. We identified all the sources having a signal-to-noise ratio |$\ge 3$| and |$\ge 2$| in these median frames for LCO and NOT, respectively, using the sep² package (Barbary et al. 2016), which is based on the SExtractor software (Bertin & Arnouts 1996). Fig. 1 shows the median image in the r’-band obtained from 2024 NOT data, centred around the coinciding radio and optical locations of J2055, marked in red and yellow, respectively.

We performed systematic aperture photometry on all the detected sources using sep, with aperture radii of 1.2 and |$1.5 \times$| the average full-width at half maximum (FWHM) for the LCO and NOT data, respectively. To improve the accuracy of our photometry, we utilized the astrosource package³ (Fitzgerald et al. 2021) to select the 8–10 most stable and brightest stars for each optical filter (g’, r’, and i’) and data set (2023 LCO, 2023 NOT, and 2024 NOT). We used these stars, with variability rms amplitudes of |$\simeq 0.004$|–|$0.01 \ \mathrm{mag}$| and magnitudes between 16 and 18.5, as comparison stars to obtain the highest precision photometry for our target, J2055.

2.2 Spectroscopy

We observed J2055 with the 10.4-m Gran Telescopio Canarias (GTC) on the night of 2024 August 1 (from MJD 60523.963626 to 60524.152712). We obtained 18 OSIRIS + long-slit spectra with an exposure time of 935 s each, at airmass 1.03–1.23 and under good seeing (⁠|$\simeq$|0.6 arcmin) and weather (clear sky) conditions. We used the R2500V grism with a central wavelength of 5185 Å and a slit width of 1 arcmin, covering the 4500–6000 Å spectral range. Together, our spectra cover 4.5 uninterrupted hours, corresponding to 94 per cent of the pulsar’s orbit.

We applied standard calibration procedures (bias and spectroscopic flat corrections) within iraf. We optimally extracted sky-subtracted spectra using starlink/pamela to account for significant tilt (Marsh 1989). We calibrated the resulting spectra in wavelength within molly, using 18 identified lines from a collated set of three arc spectra (Ne, HgAr, and Xe lamps) taken on the same evening. The wavelength scale was well-fit with a 4-term polynomial (r.m.s. 0.03 Å), with a central dispersion of about 0.80 Å px|$^{-1}$|⁠. From the 5577 Å (sky) and 5461 Å (arc) lines, we estimate a spectral resolution of 3.1 and 3.0 Å, respectively (i.e. a dimensionless resolution of |$R \simeq 1800$|⁠).

3 RESULTS

3.1 Optical light curves of the redback PSR J2055|$+$|1545

The mid-exposure UTC times of the frames were converted into the TDB coordinate system. To verify whether the orbital period of J2055 had significantly deviated from the known value of |$P_\mathrm{orb}=0.200725452(1) \ \mathrm{d}$| (Lewis et al. 2023, hereafter L23), we conducted a phase-dispersion minimization periodicity search (Stellingwerf 1978) on the LCO data.⁴ The best photometric period obtained was |$0.200725(5) \ \mathrm{d}$|⁠, which is fully consistent with the value found by L23. Therefore, we adopted their orbital period to phase-fold optical light curves and colours of J2055 both for 2023 NOT/LCO and 2024 NOT data sets (shown in the left and right panels of Fig. 2, respectively). We set phase 0 to correspond to the time of the companion’s inferior conjunction, |$T_\mathrm{0}=60523.9866(3) \ \mathrm{MJD}$|⁠, as determined from the optical spectra of J2055 (see Section 3.2 for details). Given the larger size of the LCO data set compared to NOT (see Table 1), we phase-binned the LCO light and colour curves into 15 bins to facilitate comparison with the NOT observations. To do so, we computed the average magnitude over all the points in the corresponding phase bin, with their standard deviation as uncertainty.

As shown in Fig. 2, the optical light curves of J2055 exhibit the same periodic modulation in both 2023 and 2024, with a single flux maximum per orbit and peak-to-peak amplitudes of 0.6, 0.5, and |$0.4 \ \mathrm{mag}$| in the g’, r’, and i’ bands, respectively. We also observe variable (g’ − r’) and (r’ − i’) colours along the orbit in both epochs, with maxima occurring around the companion’s superior conjunction (phase 0.5). After correcting for extinction the NOT colours observed at phase 0 and 0.5 using a colour excess of |$E(g-r)=0.07\pm 0.01$| (Green et al. 2019) and matching them to the low-mass spectral templates of Allard, Homeier & Freytag (2011), we estimated the companion temperatures at inferior and superior conjunctions, respectively.⁵ For such temperature estimates, we used only data obtained with the 2.56-|$\mathrm{m}$| NOT telescope, as they have smaller magnitude errors compared to those from the 1-|$\mathrm{m}$| LCO. From the 2023 data, we derived intrinsic colours of |$(g^{\prime }-r^{\prime }) = 0.66 \pm 0.05 \ \mathrm{mag}$| at phase 0 and |$(g^{\prime }-r^{\prime }) = 0.45 \pm 0.05 \ \mathrm{mag}$| at phase 0.5, corresponding to temperatures of |$T_{\mathrm{inf}} = 5300 \pm 200 \ \mathrm{K}$| and |$T_{\mathrm{sup}} = 5900 \pm 200 \ \mathrm{K}$|⁠, respectively. In the 2024 data set, we found intrinsic colours of |$(g^{\prime }-r^{\prime }) = 0.50 \pm 0.05$| and |$(g^{\prime }-r^{\prime }) = 0.37 \pm 0.05$| at inferior and superior conjunctions, respectively, which correspond to temperatures of |$T_{\mathrm{inf}} = 5700 \pm 175 \ \mathrm{K}$| and |$T_{\mathrm{sup}} = 6175 \pm 200 \ \mathrm{K}$|⁠. These values are consistent with those derived from the 2023 data.

The features described above strongly suggest that the companion star of J2055 is mildly heated by the pulsar wind (see Section 1). The consistency between the 2023 and 2024 observations indicates that this irradiated state persisted from 2023 July to 2024 August, without any state change in the system. Interestingly, the light curve shows a clearly asymmetric flux maximum at phase |$\simeq 0.4$|⁠, anticipating the companion’s superior conjunction, where the optical flux in irradiated spiders typically peaks. Additionally, a local maximum is observed at the descending node of the companion (phase 0.75), which appears sharper in the r’ and i’ bands compared to the g’-band. In Section 4, we explain this complex behaviour by including a hotspot component in our optical light-curve modelling. Subsequently, we discuss the implications of our results in the context of other observed RB systems (see Section 5).

3.2 Spectroscopic results from the redback PSR J2055|$+$|1545

The optical spectra of J2055’s companion are consistent with a relatively typical G-dwarf star, which is lightly irradiated by the pulsar wind. A myriad of metallic line features are visible throughout the spectra (see Fig. 3), including the Mg i triplet at 5167–5183 Å and various strong Fe i and Ca i lines from 4900 to 5400 Å. These metallic features vary in strength throughout the orbit, appearing strongest around phase 0, when the cold face of the companion is visible. The H|$\beta$| line is also a prominent feature, and shows a much more subtle, and reversed, trend – peaking in strength at phase 0.5, when we see the hot face.

We measured the temperature of the companion throughout its orbit using optimal subtraction (Marsh, Robinson & Wood 1994) between the normalized spectra of J2055 and a set of template spectra, as implemented by the astra package.⁶ This optimizes a scaling factor |$f_\mathrm{star}$| to minimize residuals between the target and template spectra, accounting for contributions from non-stellar flux (which we define as |$f_\mathrm{veil} = 1-f_\mathrm{star}$|⁠). The spectra of J2055 were first shifted to zero velocity before being averaged in 4 phase bins of a quarter phase in width, centred around |$\phi = 0$|⁠, 0.25, 0.5, and 0.75. We used a set of templates created from the BT-Settl library of synthetic spectra (Allard et al. 2011) covering the temperature range |$2600 \le T_\mathrm{eff} \le 10000$| K, broadened to match the instrumental resolution. Thus, the results of optimal subtraction against these templates provide |$\chi ^2$| (and |$f_\mathrm{star}$|⁠) as a function of |$T_\mathrm{eff}$|⁠. We then fit the minimum of this function in order to estimate both the temperature of the companion and its uncertainties, using the same approach detailed in section 2.3 of Simpson et al. (2025).

We measured temperatures using only the highest signal regions of the spectra – specifically, in the range 4820–5870 Å, as indicated in Fig. 3. From inferior conjunction (⁠|$\phi =0$|⁠), we determined an effective temperature of |$T_\mathrm{inf} = 5749 \pm 34$| K, and from superior conjunction (⁠|$\phi =0.5$|⁠), we determined an effective temperature of |$T_\mathrm{sup} = 6106 \pm 35$| K, or a spectral type ranging from G3 to F9. We also measured temperatures around the first and second points of quadrature (i.e. |$\phi =0.25$| and |$\phi =0.75$|⁠) of |$T_\mathrm{q1} = 5868 \pm 37$| K and |$T_\mathrm{q2} = 5879 \pm 39$| K, respectively, in excellent agreement with each other. We found the stellar flux contribution |$f_\mathrm{star}$| to cover the range of 0.82–0.92, with a maximum value at |$\phi = 0$| and a minimum value at |$\phi = 0.5$|⁠. This indicates a contribution of non-stellar flux or ‘veiling’ of approximately 10–20 per cent over the full orbit (i.e. |$f_\mathrm{veil} \simeq 0.1-0.2$|⁠). The full optimal subtraction fits and residual spectra for all four phase bins are presented in Fig. A1.

While |$T_\mathrm{inf}$| and |$T_\mathrm{sup}$| are in excellent agreement with the photometric temperatures from the simultaneous 2024 data, the increased precision means they are no longer consistent with the photometric temperatures from the 2023 data. This would appear to be indicative of changes in the system between the two epochs, potentially in the strength of the irradiation, or the size and location of hotspots. Additionally, the near-identical temperatures at both points of quadrature would seem to imply J2055’s companion lacks asymmetric irradiation. However, looking at the temperatures measured from individual spectra (presented in Fig. 4), it is clear the temperature maximum occurs slightly before phase 0.5. This suggests the early light-curve maximum (Fig. 2) may be the result of asymmetric irradiation on top of a maximum from ellipsoidal modulation at |$\phi = 0.25$|⁠. Both the asymmetries present, and the possibility of long-term variability are discussed further in Section 5.2.

Radial velocities from J2055 were measured in two stages. First, the cross-correlation was computed between the observed spectra and the BT-Settl templates using the full range of absorption line features present, with the exception of the Na i 5890 + 5896 Å doublet (which is contaminated by interstellar absorption). This initial cross-correlation was fit with a sinusoid (with the orbital period fixed to the value from L23) to obtain a preliminary orbital solution of |$K_2 \simeq 382 {\mathrm{\, km\, s^{-1}}}{}$|⁠, |$\gamma \simeq 40 {\mathrm{\, km\, s^{-1}}}{}$|⁠, and |$T_0 \simeq 60523.987$| MJD – where |$K_2$| is the radial velocity curve semi-amplitude, |$\gamma$| is the systemic velocity, and |$T_0$| is the time of companion inferior conjunction. Using this, we applied a careful line-by-line approach (astra’s linefitmc method) to separately fit the H |$\beta$| 4861 Å line and the Mg i 5167+5172 + 5183 Å triplet, in narrow windows around the expected radial velocities. We also computed the cross-correlation against a 5700 K template (corresponding to the measured |$T_\mathrm{inf}$|⁠), searching around this orbital solution, over the remainder of the metallic lines in the same wavelengths used for optimal subtraction. Then, using MCMC sampling, as implemented by emcee (Foreman-Mackey et al. 2013), we fit the measured velocities to determine robust values and errors for |$K_2$|⁠, |$\gamma$|⁠, and |$T_0$|⁠. Thus, we obtained three radial velocity curves from J2055: one from line-fitting of H|$\beta$|⁠, one from line-fitting the Mg i triplet, and one from cross-correlation over the other metallic lines in the range of 4820–5870 Å.

The multispecies radial velocity curves from J2055 are presented in Fig. 4. From cross-correlation over the wide range of strong metallic absorption lines (excluding Mg i), we find a precise radial velocity curve semi-amplitude of |$K_\mathrm{2, metals} = 385 \pm 3 {\mathrm{\, km\, s^{-1}}}{}$|⁠. From line-fitting of the Mg i triplet, we measure a slightly lower and less precise (but still consistent) |$K_\mathrm{2, Mg\, {\small I}} = 380 \pm 4 {\mathrm{\, km\, s^{-1}}}{}$|⁠, while from H|$\beta$|⁠, we find |$K_\mathrm{2, H\beta } = 367 \pm 9 {\mathrm{\, km\, s^{-1}}}{}$|⁠. The relevant corner plots for all three fits are shown in Fig. A2. The difference between |$K_\mathrm{2, H\beta }$| and |$K_\mathrm{2, metals}$| (and also |$K_\mathrm{2, Mg\, {\small I}}$|⁠) shows a clear separation between the radial velocities measured from different absorption-line species on the surface of J2055’s companion. The fact that |$K_\mathrm{2, metals} \gt K_\mathrm{2, H\beta }$| is consistent with Balmer absorption lines being stronger towards the irradiated face of the companion, as has been observed in other spider systems (e.g. Linares et al. 2018; Simpson et al. 2025).

The systemic velocity, |$\gamma$|⁠, and time of companion inferior conjunction, |$T_0$|⁠, are consistent between the three fits within their uncertainties. The most precise values are obtained from the cross-correlation results: |$\gamma _\mathrm{metals} = 42 \pm 2 {\mathrm{\, km\, s^{-1}}}{}$| and |$T_\mathrm{0, metals} = 60523.9866 \pm 0.0003$| MJD. This |$T_0$| differs from a simple projection of L23’s timing solution to the 2024 observational epoch by almost 7|$\sigma$|⁠, corresponding to 1 per cent of J2055’s orbit. We expect this discrepancy arises from J2055’s significant orbital period variations, which can dominate the timing solution’s uncertainties over long time-scales. Consequently, as mentioned in Section 3.1, we used our own |$T_\mathrm{0, metals}$| to phase-fold the photometry rather than |$T_\mathrm{asc}$| fromL23.

For the metal-line radial velocities, the reduced |$\chi ^2$| (i.e. |$\chi ^2_\nu$|⁠) of the fit is slightly over 1: |$\chi ^2_\mathrm{\nu , metals} = 1.47$|⁠, while for the H|$\beta$| fits, |$\chi ^2_\mathrm{\nu , H\beta } = 0.76$|⁠. For the Mg i fit, |$\chi ^2_\mathrm{\nu , Mg\, {\small I}} = 1.04$|⁠. This suggests that the measurement errors on the H|$\beta$| radial velocities are slightly overestimated, while the cross-correlation-based metal radial velocity measurement errors are slightly underestimated. Alternatively, |$\chi ^2_\mathrm{\nu , metals} \gt 1$| could imply the metal sinusoidal model fits do not fully capture the data – considering the effect of irradiation on the centre of light of the absorption features, this is more likely the case. Indeed, the effect of irradiation will distort the observed radial velocity curves, and may be the cause of the apparent trends in the residuals, where the radial velocities depart from a sinusoid. As such, to obtain a more conservative estimate of the parameter errors, the radial velocity errors for each fit have been scaled to obtain|$\chi ^2_\nu = 1$|⁠.

4 LIGHT-CURVE MODELLING

We modelled the light curves using the stellar binary light-curve synthesis code icarus (Breton et al. 2012), with the atmosphere grids generated from the atlas9 code (Kurucz 1993). The three photometric data sets, LCO 2023, NOT 2023, and NOT 2024, were converted from AB apparent magnitudes to flux densities, using the zero-point flux density of 3631 Jy for the SDSS g’, r,’ and i’ filters. The orbital phase 0 was defined as at inferior conjunction of the companion. In order to ensure that each data set had equal weight, we binned the data so that each data set had 15 bins. We then fitted these three data sets with a linked sampling algorithm using the nested sampler dynesty (Skilling 2004; Skilling 2006; Feroz, Hobson & Bridges 2009; Speagle 2020; Koposov et al. 2024), similar to what was done in Sen et al. (2024), where we simultaneously fitted all data sets while only allowing some of the parameters to vary independently between the data sets. The rest of the parameters were linked, meaning that they were sampled such that these parameters varied at different steps of the sampler, but were the same for all data sets at each step.

4.1 Model parameters

Icarus requires 11 parameters to be specified for the direct irradiation models, where only the effects of gravity darkening and irradiation contribute to the companion’s effective temperature. Four additional parameters are required for hotspot models to specify the size, extent, and location of the spot. We held three of the direct irradiation parameters constant. We assumed a tidally locked system and set the co-rotation factor |$\omega = 1$|⁠, and fixed the gravity darkening coefficient |$\beta = 0.08$| as that corresponds to low-mass companions with a convective envelope (Lucy 1967). From L23, we fixed the orbital period to |$P_\text{orb} = 0.200725452(1)$| d. To model the asymmetry of the light curves, we fitted the data to hotspot models. We determined the location of an equatorial hotspot by finding the orbital phase where the symmetric model underpredicted the flux the most, which was at |$\phi = 0.35$|⁠. From this, we found the corresponding longitude of the companion hotspot.

4.1.1 Prior distributions and spectroscopic constraints

We linked the following parameters, as they are not expected to change on month- to year-timescales: the semi-major axis of the pulsar |$x_1$|⁠, inclination i, projected radial velocity semi-amplitude of the companion |$K_2$|⁠, filling factor f, base temperature |$T_\text{base}$|⁠, distance D, and extinction in the V band |$A_V$|⁠, which are reported in Table 2. From |$x_1$| and |$P_\text{orb}$|⁠, we derived the projected radial velocity semi-amplitude of the pulsar, |$K_1$|⁠. We used this with |$K_2$| to derive the mass ratio q with the constraint from pulsar timing and input it into Icarus. By doing so, we applied a uniform prior on |$x_1$| using the reported |$x_1 = 0.5996750(1)$| lt-s from L23. The other parameters were used directly as inputs. The prior on |$K_2$| centred around |$385 \pm 3 {\mathrm{\, km\, s^{-1}}}{}$| was derived from spectroscopic analysis, as explained in Section 3.2.⁷ Given that edge-on systems are more likely to be detected, we applied a uniform prior on |$\cos i$|⁠. The prior for the filling factor, defined as |$f\equiv r_{\mathrm{nose}}/r_{L_{1}}$|⁠, was also uniform between 0 and 1. |$T_\text{base}$| had a uniform prior between 1000 and 10 000 K. The other uniform linked prior was D, which was between 1 and |$10 \ \mathrm{kpc}$|⁠. We assigned to the last linked parameter, |$A_V$|⁠, a Gaussian prior determined by the colour excess of |$E(g-r) = 0.07 \pm 0.01$| from the Green et al. (2019) dust maps.

The rest of the parameters were unlinked and kept independent. For each data set, these include the irradiation and hotspot temperatures, |$T_\text{irr}$| and |$T_\text{spot}$|⁠, respectively, as well as the radius of the spot |$R_\text{spot}$|⁠. For the spot parameters, we applied uniform prior distributions, as seen in Table 2. We allowed |$T_\text{spot}$| to vary from |$0\,{\rm and}\,1000$| K and we allowed the radius to extend up to half of the star. For |$T_\text{irr}$|⁠, we allow the prior distribution to vary from |$0\,{\rm and}\,10\,000$| K. We include an additional constraint on the observed |$T_\text{inf}$| of the companion for one of our fits. We apply a flat prior of |$5746 \pm 165$| K using the |$3 \sigma$| range of the results from optimal subtraction on the single spectrum closest to phase 0.

4.2 Best-fitting model results

We find that our two linked models are consistent within |$1\sigma$| for all but two of the linked parameters, for the radius of the spot, and for most of the derived parameters, as seen in Table 3. Among the independent parameters, |$R_\text{spot}$| and |$T_\text{spot}$| are also compatible within |$1\sigma$| between the same epochs of the two fits. The differences in the two fits arise from the independent parameters, which control the effective temperature of the companion. From the fit without any temperature constraints, we find that the model |$T_\text{inf}$| is not within |$5\sigma$| of the spectroscopic |$T_\text{inf}$|⁠, depending on the data set. Similarly for |$T_\text{sup}$|⁠, the model and spectroscopic temperatures also differ by |$5\sigma$|⁠. When the |$T_\text{inf}$| constraint is implemented during the fitting, we find that the linked |$T_\text{base}$| and unlinked |$T_\text{irr}$|⁠, and in turn the derived |$T_\text{inf}$| and |$T_\text{sup}$|⁠, increase. In addition to this, |$A_V$| increases to compensate for the higher temperature, so that the model flux is not overpredicted.

Between the data sets, we find that the hotspot seems to shrink in size from 2023 to 2024, differing more than |$1\sigma$| from each other, while the temperature decreases over time. The temperature and radius of the hotspot for the LCO and NOT 2023 data sets are consistent within |$1\sigma$| from each other, as is |$T_\text{sup}$|⁠. On the other hand, we notice that the irradiating temperature |$T_\text{irr}$| estimated from LCO 2023 is higher by more than |$2-3\sigma$| with respect to both NOT data sets, depending on whether the model included the |$T_\text{inf}$| constraint or not. As expected, we see that |$T_\text{inf}$| for all epochs for the fit with the |$T_\text{inf}$| constraint are consistent to |$1\sigma$|⁠, but we also note this is the case for the fit without this constraint. The fit without temperature constraints also has |$T_\text{sup}$| values that are consistent at less than |$1\sigma$|⁠, in contrast to the other fit, where the LCO 2023 and NOT 2024 |$T_\text{sup}$| values are consistent only at the |$1.5\sigma$| level.

We find that the mass estimates |$M_{1}$| and |$M_{2}$| for the pulsar and the companion, respectively, are similarly precise for both fits. For the temperature parameters, the |$+1\sigma$| relative uncertainties in the fit with the |$T_\text{inf}$| constraint are reduced by approximately 1–2  per cent compared to the unconstrained fit. While the |$A_V$| posterior for the constrained fit does not follow the prior as well as the unconstrained fit and |$T_{\mathrm{base}}$| increases in the constrained fit, we find that the other linked parameters are consistent between the two fits. Both the reduced chi-squared values are of |$\chi ^{2}_{\nu }\simeq 1.6$|⁠, with the constrained fit more consistent with the spectroscopy given that we use a spectroscopic constraint. Therefore, our best fit is the one with the |$T_\text{inf}$| constraint, and our derived best-fitting neutron star mass is |$1.7^{+0.4}_{-0.1} \ \mathrm{M}_{\odot }$|⁠. We show the light curves for this fit in Fig. 5.

5 DISCUSSION

5.1 A new mildly-irradiated redback

The optical light curves of J2055 do not indicate any state change between 2023 July–November and 2024 August, as we can see in Fig. 2. In both epochs, this system consistently shows variable colours and a single asymmetric broad light maximum per orbit at phase |$\simeq 0.4$|⁠, slightly anticipating companion superior conjunction at phase 0.5. This strongly suggests that the companion star of J2055 is heated by the pulsar wind with an asymmetric pattern. This is further supported by the effective temperature curve shown in Fig. 4, which peaks slightly before phase 0.5.

Furthermore, we measure peak-to-peak amplitudes of 0.6, 0.5, and |$0.4 \ \mathrm{mag}$| in g’, r’, and i’, respectively, which are lower than the typical amplitudes of |$\gtrsim 1 \ \mathrm{mag}$| observed from irradiated redbacks (see e.g. Linares et al. 2018 for PSR J2215|$+$|5135 and Romani & Shaw 2011 for PSR J2339–0533). We also observe a small hump across the companion descending node (phase 0.75), which appears sharper in the r’ and i’ bands compared to g’. This is likely produced by an underlying ellipsoidal modulation, still noticeable in the redder bands but overwhelmed in g’ where the irradiation is stronger, and is confirmed by the model without irradiation shown in the right panel of Fig. 5. All these features indicate that the companion star of J2055 is mildly heated by the pulsar wind, lying in-between the ellipsoidal and the strong irradiation regimes (Turchetta et al. 2023).

A few other RB systems show optical phenomenology similar to that of J2055. In particular, PSR J1048|$+$|2339 (henceforth called J1048) has been observed to change from an ellipsoidal to an irradiated state in less than two weeks (Yap et al. 2019). The irradiation-dominated optical light curves of J1048 show the same shape as J2055’s light curves, with asymmetric flux maxima and small humps at about phase 0.75. Interestingly, J2055 seems to be much more stable than J1048, without any clear state transition during our 4-month-long LCO monitoring. Among other RBs, PSR J1306–40 (J1306, Swihart et al. 2019) and the two transitional MSPs PSR J1023|$+$|0038 and PSR J1227–4853 (J1023 and J1227, respectively, Stringer et al. 2021⁸) exhibit optical light curves closely resembling those of J2055. All show amplitudes of |$\lesssim 0.8 \mathrm{mag}$| and asymmetric flux maxima flattening at redder bands, where the ellipsoidal variation contribution is non-negligible compared to the irradiation component.

To quantify the irradiation power of spider MSPs we can apply the pulsar spin-down to companion flux ratio parameter |$f_{\mathrm{sd}}$| (see equation 3 in Turchetta et al. 2023). Concerning J2055, using |$L_{\mathrm{sd}}=(3.83\pm 0.01) \times 10^{34} \ \mathrm{erg} \ \mathrm{s}^{-1}$| and |$P_{\mathrm{orb}}=4.81741085\pm 0.00000002 \ \mathrm{h}$| from L23, |$T_{\mathrm{base}}=5728^{+40}_{-23} \ \mathrm{K}$| and |$M_{1}+M_{2}=2.0\pm 0.2\ \mathrm{M}_{\odot }$| from our light curve modelling, we obtain a flux ratio of |$f_{\mathrm{sd}}=3.0\pm 0.1$|⁠, placed exactly in the transition region between ellipsoidal and irradiated regimes (Turchetta et al. 2023), as we expect. We also find |$f_{\mathrm{sd}}=2.6\pm 0.2$|⁠, |$3.9\pm 0.4$| and |$4.9\pm 1.2$| for J1048, J1023, and J1227,⁹ respectively (Turchetta et al. 2023) – all consistent with the same intermediate state observed in J2055.

Furthermore, our best-fitting model of J2055’s optical light curves yields an irradiating luminosity of |$L_{\mathrm{irr}}=(1.8\pm 0.7) \times 10^{32} \ \mathrm{erg} \ \mathrm{s}^{-1}$|⁠, which remains consistent across the three data sets – LCO 2023, NOT 2023, and NOT 2024. Following the definition by Breton et al. (2013), we derive an irradiation efficiency relative to the spin-down luminosity of |$\epsilon _{\mathrm{irr}}\equiv L_{\mathrm{irr}}/L_{\mathrm{sd}}=0.5\pm 0.2~{{\ \rm per\ cent}}$| for this system. In comparison, J2055 irradiation efficiency is lower than the 10–30  per cent range observed in strongly irradiated spider companions (Breton et al. 2013), yet higher than the |$\simeq 0.1~{{\ \rm per\ cent}}$| of PSR J1622–0315 (Sen et al. 2024), whose light curves exhibit little to no irradiation. This further supports the conclusion that J2055’s companion is mildly irradiated by the pulsar wind.

The close resemblance of the optical light curves of J2055, J1048, and J1306 with that of J1023 and J1227 suggests that they might all be transitional MSPs observed during their rotation-powered state. We argue that these systems may show in the future a transition from the radio pulsar to the accretion disc state. Indeed, the lack of strong irradiation indicates that the magnetic pressure exerted by the pulsar wind may not be effective enough to overcome the formation of an accretion disc in these systems, in case the companion star exceeds its Roche lobe. Although we estimate for J2055 a filling factor |$f\equiv r_{\mathrm{nose}}/r_{L_{1}}$| of only |$0.74^{+0.03}_{-0.01}$| (see Table 3), the other RBs considered are also significantly under-filling their Roche lobes (Swihart et al. 2019; Yap et al. 2019; Stringer et al. 2021). In particular, Stringer et al. (2021) estimate |$f=0.94$| and 0.84 for J1023 and J1227, respectively, using the hotspot model. However, their corresponding volume-averaged filling factors are much closer to unity due to tidal distortion (Stringer et al. 2021), namely |$f_{\mathrm{VA}}=0.99$| and 0.96 for J1023 and J1227, respectively (see fig. 10 in Stringer et al. 2021). Using Icarus, we convert J2055’s filling factor into a volume-averaged filling factor of |$f_{\mathrm{VA}}=0.90\pm 0.01$|⁠, which suggests a bloated companion star that may unpredictably overfill its Roche lobe and start transferring mass.

5.2 Radial velocities and spectroscopic temperatures

The optical spectra of J2055 enabled precise measurements of the companion’s temperature throughout its orbit, with the results of optimal subtraction yielding |$T_{\mathrm{inf}}=5749\pm 34 \, \mathrm{K}$| and |$T_{\mathrm{sup}}=6106\pm 35 \, \mathrm{K}$|⁠, respectively (Section 3.2 and Fig. A1). These values are in full agreement with the less precise estimates derived from the simultaneous 2024 photometry, while they are both higher than those from the 2023 data of |$T_{\mathrm{inf}}=5300\pm 200 \, \mathrm{K}$| and |$T_{\mathrm{sup}}=5900\pm 200 \, \mathrm{K}$|⁠.

Since the temperatures measured around inferior and superior conjunction depend on both the binary inclination and the irradiating flux (Simpson et al. 2025), the observed differences between 2023 and 2024 could suggest an increase in the irradiation strength of J2055. However, the light-curve modelling presented in Section 4 indicates that |$T_{\mathrm{inf}}$| and |$T_{\mathrm{sup}}$| remain consistent across the two epochs, instead revealing a change in the size of the companion’s hotspot (see Table 3). To better constrain the inclination and base temperature (⁠|$T_\mathrm{base}$|⁠) of this system, we incorporated the spectroscopic temperature at inferior conjunction (⁠|$T_\mathrm{inf}$|⁠) as a prior in one of our linked fits, as detailed in Section 4.1.

We also estimated spectroscopic temperatures at the companion’s ascending and descending nodes for this system, obtaining |$T_\mathrm{q1} = 5868 \pm 37$| K and |$T_\mathrm{q2} = 5879 \pm 39$| K, respectively. Their close agreement, along with the early occurrence of the light curve and temperature maxima (Figs 2 and 4), suggests the presence of a light asymmetric irradiation component superimposed on an ellipsoidal modulation peak at the first quadrature. This interpretation is further supported by the light curve model without irradiation, shown in the right panel of Fig. 5 with dashed lines, which is only slightly exceeded by the asymmetric irradiation model (solid lines) at phases 0.25 and 0.75. Future observations of J2055 in a potential ellipsoidal-dominated state, similar to the scenario analysed by Yap et al. (2019) for J1048, could help disentangle and quantify these two different contributions.

As we can see from Fig. 3, J2055’s spectra show numerous metallic absorption lines, which appear most prominent around phase 0, when the cold side of the companion is visible. In contrast, the H |$\beta$| line becomes stronger around the companion superior conjunction, when we observe the companion’s hot side. As a result, the semi-amplitude of the radial velocity curve measured from the H|$\beta$| line (⁠|$K_\mathrm{2, H\beta } = 367 \pm 9 {\mathrm{\, km\, s^{-1}}}{}$|⁠) is lower than that derived from the metallic lines (⁠|$K_\mathrm{2, metals} = 385 \pm 3 {\mathrm{\, km\, s^{-1}}}{}$|⁠). This discrepancy is due to the displacement of the centre of light relative to the companion’s centre of mass, with stronger irradiation causing a more pronounced shift of the Balmer lines toward the inner surface of the companion.

The separation between the centre of light and the CoM of the companion has already been observed in a few other irradiated spiders (e.g. PSR J2215|$+$|5135, Linares et al. 2018; PSR J1810|$+$|1744, Romani et al. 2021 and J1048, Simpson et al. 2025). Here, we did not apply any ‘K-correction’ to take this effect into account. While metallic lines appear stronger on the night side of the companion, irradiation causes the continuum flux to be higher towards the day side. The combination of these two factors can result in metallic lines instead tracking the CoM reasonably well, while Balmer lines are pushed even more towards the inner face (Dodge et al. 2024). Considering this, and the fact that J2055’s companion is only lightly irradiated, the metallic line RVs were taken to be approximately representative of the movement of the companion’s CoM, and thus |$K_\mathrm{2, metals}$| was used as a prior on the CoM |$K_2$| for the light curve modelling (see Table 2).

The optical spectra of J2055 exhibit no emission features, ruling out the presence of an accretion disc in the system, as expected. If an accretion disc were present, we would expect to detect prominent double-peaked hydrogen or helium emission lines, similar to those observed in the transitional MSP J1023 during its disc state (e.g. Takata et al. 2014, Coti Zelati et al. 2014, Shahbaz et al. 2019). Interestingly, although the optical light curves of J2055 closely resemble those of J1048, the latter displays strong H|$\alpha$| emission lines in its spectra (Miraval Zanon et al. 2021; Simpson et al. 2025). This emission has been interpreted by Miraval Zanon et al. (2021) as an effect of the intrabinary shock between the pulsar wind and the material ablated in close proximity of the companion star. However, it is important to note that such features have only been observed in a few spider pulsars under poorly understood conditions (Strader et al. 2019). Therefore, the absence of H |$\alpha$| emission in J2055 does not necessarily imply the lack of an intrabinary shock in this system.

5.3 Masses, orbital parameters, and distance

We modelled the optical light curves of J2055, incorporating an equatorial hotspot component to account for the asymmetry observed in their maxima, as the symmetric irradiation model showed significant trends in the residuals. In our modelling, parameters expected to remain stable across the three data sets – LCO 2023, NOT 2023, and NOT 2024 – were linked (see Section 4.1 for details). To reduce the model degeneracy between the orbital inclination and the companion’s radial velocity semi-amplitude, we adopted a prior of |$K_\mathrm{2} = 385 \pm 3 {\mathrm{\, km\, s^{-1}}}{}$| based on our spectroscopic analysis. This is crucial for accurately determining the neutron star mass, which scales as |$M_{1}\propto K_{2}^{3}/\sin ^{3}{i}$|⁠.

We also incorporated an additional spectroscopic constraint on the observed temperature at inferior conjunction, |$T_\mathrm{inf}$|⁠, to obtain more accurate estimates of the base temperature of the companion, the strength of irradiation, and the orbital inclination from light-curve modelling. Temperature measurements obtained using optimal subtraction (Section 3.2) rely on absorption line strengths, making them independent of extinction and therefore more robust than those inferred from optical light curves alone. Both models, with and without the |$T_{\mathrm{inf}}$| constraint, provide good fits to J2055’s light curves, yielding similar reduced |$\chi ^{2}$| values of 1.59 and 1.66, respectively. However, the |$T_{\mathrm{inf}}$| derived from the ‘unconstrained’ fit is significantly lower than the spectroscopic estimate, and the uncertainties for the ‘constrained’ fit are smaller overall, as we can see in Table 3. Therefore, we adopt the fit with the |$T_{\mathrm{inf}}$| constraint as our best model, with the corresponding system parameters reported in the right section of Table 3.

Our best-fitting model shows that both the observed temperatures and the irradiating luminosity remain consistent across the three epochs, with values of |$T_{\mathrm{inf}} \simeq 5600 \, \mathrm{K}$|⁠, |$T_{\mathrm{sup}} \simeq 6200 \, \mathrm{K}$|⁠, and |$L_{\mathrm{irr}} \simeq 2 \times 10^{32} \, \mathrm{erg} \, \mathrm{s}^{-1}$|⁠, respectively. On the other hand, the companion hotspot in LCO and NOT 2023 data is both slightly warmer and slightly larger than the hotspot observed in the NOT 2024 data set. Comparing NOT 2023 to NOT 2024, the hotspot shrinks from |$54^{\circ }$| to |$33^{\circ }$| and cools by |$\sim$||$100\, \mathrm{K}$|⁠. We propose that this hotspot is produced by variable asymmetric irradiation from an intrabinary shock between the pulsar and companion winds. The location of the spot on the companion (see Table 2) can be explained by assuming that the shock is wrapped around the pulsar, as has been observed in other RB systems (Cho, Halpern & Bogdanov 2018), with the companion wind dominating over the pulsar wind (Romani & Sanchez 2016). This shock geometry would enhance the irradiating flux on the companion’s trailing edge, which accounts for the early light curve maximum observed in J2055.

Here, we present the first estimates for J2055’s orbital inclination, |$i=79^{+8}_{-13}$||$^\circ$|⁠, and neutron star mass, |$M_{1}=1.7^{+0.4}_{-0.1} \ \mathrm{M}_{\odot }$|⁠, from our best-fit model with the |$T_{\mathrm{inf}}$| constraint, indicating a fairly massive neutron star¹⁰ hosted in a moderately edge-on system. In general, the precision of neutron star mass measurements in spiders largely depends on the orbital inclination and the companion’s radial velocity semi-amplitude. As we can see in Figs B1 and B2, the area covered by |$M_{1}$| in both the unconstrained and constrained fits is determined by i, while it shows no correlation with |$K_{2}$|⁠, as the latter is tightly inferred from spectroscopy. This leads to a more accurate estimate of |$T_{\mathrm{base}}$|⁠, |$L_{\mathrm{irr}}$|⁠, and consequently i, as the observed temperatures and light curve modulation are tightly linked to these parameters. In this case, where the companion radial velocity is precisely determined, the uncertainty on the orbital inclination drives the precision of the neutron star mass measurement.

Among other parameters, we obtain a companion mass of |$M_{2}=0.29^{+0.07}_{-0.01} \ \mathrm{M}_{\odot }$|⁠, in full agreement with the median value |$0.29 \ \mathrm{M}_{\odot }$| inferred by L23. Interestingly, the distance from our best fit |$D=5.34^{+0.54}_{-0.20} \ \mathrm{kpc}$| places J2055 farther than the estimates from L23, which found distances of |$2.4 \ \mathrm{kpc}$| and |$3.7 \ \mathrm{kpc}$| using the electron density models of Yao, Manchester & Wang (2017) and Cordes & Lazio (2002), respectively. This discrepancy is not surprising, as dispersion measure distances for spider MSPs are known to systematically underestimate the true distances due to small-scale inaccuracies in the electron density models, as shown by Koljonen et al. (2024).

Spider MSPs often emit X-rays through synchrotron radiation from the intrabinary shock region (Gentile et al. 2014; Linares 2014). Using our updated |$D=5.34$| kpc, we revise the upper limit on the X-ray luminosity of J2055 (previously estimated by L23) to |$L_X \lt 1.9\times 10^{31} \ \mathrm{erg} \ \mathrm{s}^{-1}$| (0.3–10 keV). This new value is more consistent with the typical X-ray luminosities of Galactic RBs, whose distribution peaks at |$8\times 10^{31} \ \mathrm{erg} \ \mathrm{s}^{-1}$| (Koljonen & Linares 2023). Likewise, assuming the association of this RB MSP with 4FGL J2055.8|$+$|1545, we revise its |$\gamma$|-ray luminosity to |$L_\gamma = 7.8\times 10^{33} \ \mathrm{erg} \ \mathrm{s}^{-1}$| (0.1–100 GeV), which remains compatible with the typical |$\gamma$|-ray luminosity ranges of MSPs (Smith et al. 2023).

6 CONCLUSIONS

We obtained the first optical light and radial velocity curves of the companion to the RB MSP J2055. The light curve exhibits a mildly-irradiated regime with amplitudes of |$\simeq 0.4$|–|$0.6 \ \mathrm{mag}$|⁠, where the heating from the pulsar wind slightly surpasses the underlying ellipsoidal modulation. The light maximum shows a pronounced asymmetry, occurring earlier than the superior conjunction. Through optimal subtraction of the companion’s optical spectra, we accurately determine temperatures over its orbit, which show an amplitude of about |$400 \, \mathrm{K}$|⁠.

Using independent constraints on the companion’s radial velocity semi-amplitude and temperature from our spectroscopy, we simultaneously modelled three optical light curves of J2055 obtained at different epochs, linking the parameters |$T_{\mathrm{base}}$|⁠, |$L_{\mathrm{irr}}$|⁠, |$T_{\mathrm{spot}}$|⁠, and |$R_{\mathrm{spot}}$|⁠. While these parameters remained largely stable from 2023 July to 2024 August, the hotspot component exhibited a slight variation between epochs, which we attribute to an asymmetric intrabinary shock. Our analysis provides, among others, the first measurements of the orbital inclination, |$i=79^{+8}_{-13}$||$^\circ$|⁠, and neutron star mass, |$M_{1}=1.7^{+0.4}_{-0.1} \ \mathrm{M}_{\odot }$|⁠, of J2055, favouring a moderately inclined system hosting a fairly massive neutron star. Additionally, the inferred distance of |$5.3 \ \mathrm{kpc}$| places J2055 farther than the dispersion measure estimates of 2.4–|$3.7 \ \mathrm{kpc}$| derived from radio timing of the MSP.

The distinctive shape of J2055’s optical light curve and its mild level of irradiation closely resemble those observed in the transitional MSPs PSR J1023|$+$|0038 and PSR J1227–4853 during their rotation-powered states. These similarities, combined with a Roche-lobe filling factor comparable to that of the two transitional systems, suggest that J2055 could potentially transition to a disc accretion-powered state in the future.

ACKNOWLEDGEMENTS

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 101002352). This work makes use of observations from the Las Cumbres Observatory global telescope network (we thank L. Storrie-Lombardi and N. Volgenau for their support). Based on observations made with the Nordic Optical Telescope, operated jointly by Aarhus University, the University of Turku and the University of Oslo, representing Denmark, Finland and Norway, the University of Iceland and Stockholm University. Based on observations made with the GTC telescope, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias, under Director’s Discretionary Time (GTC2024-249). We thank T. Marsh for the use of molly and pamela. MT thanks K. Koljonen for a discussion on the irradiation strength in spider systems, and how it affects the shape of their optical light curves. JC acknowledges support by the Spanish Ministry of Science via the Plan de Generación de Conocimiento through grant PID2022-143331NB-100. RPB is supported by the UK Science and Technology Facilities Council (STFC), grant number ST/X001229/1.

DATA AVAILABILITY

The raw LCO and NOT images with bias and flats frames used for data reduction can be obtained by contacting M. Turchetta. The raw GTC science and arc spectra with corresponding data reduction frames can be obtained by contacting J. Simpson.

Footnotes

REFERENCES

APPENDIX A: DETAILS OF SPECTRAL ANALYSIS

APPENDIX B: LIGHT-CURVE MODELLING CORNER PLOT