Calibrating spectrum to photometry

[tjtakys]

Hi, I am currently using Prospector to fit both photometry and spectrum simultaneously for several high-z galaxies. The spectrum I am analyzing comes from NIRSpec with a medium grating. While individual channels in the spectrum are noisy and do not show a clear continuum (left figure shows an example spectrum), summing across many channels makes the continuum detection. However, when convolving the spectrum with filter transmissions and comparing it to photometry, I observe up to a 50% discrepancy (right figure shows the relative difference for several galaxies).

To address these discrepancies, I use optimize_speccal with a second-order polynomial for spectral calibration. However, in some cases, the spectrum appears to be over-calibrated, which may strongly influence the derived parameters, such as SFH, Av, and gas logZ. This is a concern for me.

model_params = {}
# common parameters
model_params["imf_type"] = {'N':1, 'isfree':False, 'init':1} # 0:Salpeter, 1:Chabrier, 2:Kroupa
model_params["logzsol"] = {'N':1, 'isfree':True, 'init':-0.5, 'units':'log (Z/Zsun)', 'prior':priors.TopHat(mini=-2, maxi=0.2)}

# Non-parametric SFH
model_params.update(TemplateLibrary["continuity_sfh"])
nbin = 6
agelims = [0.0, 7.0] + np.linspace(start=7, stop=np.log10((cosmo.age(z=zspec)-cosmo.age(z=20)).to('yr').value), num=nbin)[1:].tolist()
agebins = np.array([agelims[:-1], agelims[1:]]).T

# This is the *total*  mass formed, as a variable
model_params["logmass"] = {"N":1, "isfree":True, "init":10, 'units':'Msun', 'prior':priors.TopHat(mini=8, maxi=12)}
# This will be the mass in each bin.  It depends on other free and fixed parameters.  Its length needs to be modified based on the number of bins
# This converts from an array of log_10(SFR_j / SFR_{j+1}) and a value of log10(\Sum_i M_i) to values of M_i.  j=0 is the most recent bin in lookback time.
model_params["mass"] = {'N':nbin, 'isfree':False, 'init':1e6, 'units':r'M$_\odot$', 'depends_on':transforms.logsfr_ratios_to_masses}
# This gives the start and stop of each age bin.  It can be adjusted and its length must match the lenth of "mass"
model_params["agebins"] = {'N':nbin, 'isfree':False, 'init':agebins, 'units':'log(yr)'}
# This controls the distribution of SFR(t) / SFR(t+dt). It has NBINS-1 components.
model_params["logsfr_ratios"] = {'N':nbin-1, 'isfree':True, 'init':np.full(nbin-1, 0.0),
                                    'prior':priors.StudentT(mean=np.full(nbin-1, 0.0),
                                                            scale=np.full(nbin-1, 0.3),
                                                            df=np.full(nbin-1, 2))}

# redshift
model_params["zred"] = {'N':1, 'isfree':False, 'init':zspec, 'units':'redshift'}

# Dust attenuation (diffuse: Kriek & Conroy 2013 + birth cloud: index=-1)
model_params["dust_type"] = {'N':1, 'isfree':False, 'init':4, 'units':'FSPS index'} # Kriek & Conroy 2013
model_params["dust_tesc"] = {'N':1, 'isfree':False, 'init':7.0, 'units':'log(yr)'} 
model_params["dust1"] = {'N':1, 'isfree':False, 'init':0.0, 'units':'optical depth towards young stars', 'depends_on':transforms.dustratio_to_dust1}
model_params["dust2"] = {'N':1, 'isfree':True, 'init':0.2, 'units':'optical depth for all stars at 5500AA', 'prior':priors.TopHat(mini=0.0, maxi=4.0)}
model_params["dust_ratio"] = {'N':1, 'isfree':True, 'init':1.0, 'units':'ratio of birth-cloud to diffuse dust', 'prior':priors.ClippedNormal(mini=0.0, maxi=2.0, mean=1.0, sigma=0.3)}
model_params["dust_index"] = {'N':1, 'isfree':False, 'init':-0.7, 'units':'power-law multiplication of Calzetti', 'prior':priors.TopHat(mini=-1.0, maxi=0.4)}
model_params["dust1_index"] = {'N':1, 'isfree':False, 'init':-1.3, 'units':'power-law multiplication of Calzetti'}

# Nebular
model_params.update(TemplateLibrary["nebular"]) 
model_params["nebemlineinspec"] = {'N':1, 'isfree':False, 'init':False} 
model_params['eline_sigma'] = {'N': 1, 'isfree':True, 'init':150.0, 'units':'km/s', 'prior':priors.TopHat(mini=50, maxi=300)}
model_params["gas_logz"] = {'N':1, 'isfree':True, 'init':0.0, 'units':'log Z/Zsun', 'prior':priors.TopHat(mini=-2, maxi=0.5)}
model_params["gas_logu"] = {'N':1, 'isfree':True, 'init':-2.0, 'units':'Q_H/N_H', 'prior':priors.TopHat(mini=-4, maxi=-1)}
    
# smoothing
model_params.update(TemplateLibrary["spectral_smoothing"])
model_params['fftsmooth'] = {'N': 1, 'isfree': False, 'init': True}
model_params['sigma_smooth'] = {'N':1, 'isfree':True, 'init':200, 'units':'km/s', 'prior':priors.TopHat(mini=50, maxi=200)} # sigma, NOT FWHM

# continuum optimize
model_params.update(TemplateLibrary["optimize_speccal"])
model_params['polyorder'] = {'N': 1, 'isfree': False, 'init': 2} # 12 is too much?
model_params['spec_norm'] = {'N': 1, 'isfree': False, 'init': 1.0, 'units': 'f_true/f_obs', 'prior':priors.Normal(mean=1.0, sigma=0.1)} 

model = PolySpecModel(model_params)

Below, I include SED plots for two galaxies. In each plot:
• Gray line: The intrinsic best-fit spectrum (without spec cal).
• Blue line: The full spectrum after spec cal.

# full sed 
obs_copy = obs.copy()
obs_copy['spectrum'] = None
obs_copy['wavelength'] = None
model_wl = sps.wavelengths * (1 + zspec) / 1e4
model_fullspec, _, _ = model.predict(result["bestfit"]["parameter"], obs_copy, sps=sps)
# nebular line
obs["wavelength"] = model._outwave
obs["spectrum"] = np.ones_like(model._outwave)
model.cache_eline_parameters(obs)
spec_neb = model.predict_eline_spec(line_indices=model._use_eline, wave=model._outwave).sum(axis=1)

ax.step(model_wl, model_fullspec+spec_neb, lw=0.5, color='gray', label="Model spec (full)")
ax.step(wspec, result["bestfit"]["spectrum"], lw=0.5, color='tab:orange', label="Best spec") # intrinsic spectrum

The first case shows minimal differences between the intrinsic and calibrated spectra, while the second case exhibits significant wavelength-dependent adjustments. Since there is no strong wavelength-dependent offset in the actual photometry-spectra comparison, I believe this large adjustment is incorrect. I am concerned that this over-calibration is skewing the derived physical parameters.

Questions:

I am considering the following approaches to address this issue:

1. Use even lower polynomial (0 or 1-order) --> But after some experimets, even the polyprder=1 case was found to cause similar problems.
2. Setting poly_regularization to a value greater than 0. However, I am unsure how to determine an appropriate value for this parameter.
3. Fit the major emission lines (e.g., Hα, Hβ, [OIII]5007) with Gaussians before performing the SED fit, subtract the continuum component, and mask the regions without emission lines. Then, input this processed spectrum into Prospector and use LineSpecModel with linespec_scaling=1 fixed during fitting. However, as I couldn’t find an example demonstration, I’m uncertain if this approach is correct.

Which approach would you recommend? Or do you have other suggestions for mitigating the effects of over-calibration while ensuring accurate physical parameter estimation?

Thank you in advance!